Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer
2013-01-01
Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…
Using the Ridge Regression Procedures to Estimate the Multiple Linear Regression Coefficients
Gorgees, HazimMansoor; Mahdi, FatimahAssim
2018-05-01
This article concerns with comparing the performance of different types of ordinary ridge regression estimators that have been already proposed to estimate the regression parameters when the near exact linear relationships among the explanatory variables is presented. For this situations we employ the data obtained from tagi gas filling company during the period (2008-2010). The main result we reached is that the method based on the condition number performs better than other methods since it has smaller mean square error (MSE) than the other stated methods.
Olive, David J
2017-01-01
This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...
Yoneoka, Daisuke; Henmi, Masayuki
2017-06-01
Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Quinino, Roberto C.; Reis, Edna A.; Bessegato, Lupercio F.
2013-01-01
This article proposes the use of the coefficient of determination as a statistic for hypothesis testing in multiple linear regression based on distributions acquired by beta sampling. (Contains 3 figures.)
Recursive Algorithm For Linear Regression
Varanasi, S. V.
1988-01-01
Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.
Standards for Standardized Logistic Regression Coefficients
Menard, Scott
2011-01-01
Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…
Modified Regression Correlation Coefficient for Poisson Regression Model
Kaengthong, Nattacha; Domthong, Uthumporn
2017-09-01
This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).
Chaurasia, Ashok; Harel, Ofer
2015-02-10
Tests for regression coefficients such as global, local, and partial F-tests are common in applied research. In the framework of multiple imputation, there are several papers addressing tests for regression coefficients. However, for simultaneous hypothesis testing, the existing methods are computationally intensive because they involve calculation with vectors and (inversion of) matrices. In this paper, we propose a simple method based on the scalar entity, coefficient of determination, to perform (global, local, and partial) F-tests with multiply imputed data. The proposed method is evaluated using simulated data and applied to suicide prevention data. Copyright © 2014 John Wiley & Sons, Ltd.
Sergei Vladimirovich Varaksin
2017-06-01
Full Text Available Purpose. Construction of a mathematical model of the dynamics of childbearing change in the Altai region in 2000–2016, analysis of the dynamics of changes in birth rates for multiple age categories of women of childbearing age. Methodology. A auxiliary analysis element is the construction of linear mathematical models of the dynamics of childbearing by using fuzzy linear regression method based on fuzzy numbers. Fuzzy linear regression is considered as an alternative to standard statistical linear regression for short time series and unknown distribution law. The parameters of fuzzy linear and standard statistical regressions for childbearing time series were defined with using the built in language MatLab algorithm. Method of fuzzy linear regression is not used in sociological researches yet. Results. There are made the conclusions about the socio-demographic changes in society, the high efficiency of the demographic policy of the leadership of the region and the country, and the applicability of the method of fuzzy linear regression for sociological analysis.
Correlation and simple linear regression.
Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G
2003-06-01
In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.
Multiple linear regression analysis
Edwards, T. R.
1980-01-01
Program rapidly selects best-suited set of coefficients. User supplies only vectors of independent and dependent data and specifies confidence level required. Program uses stepwise statistical procedure for relating minimal set of variables to set of observations; final regression contains only most statistically significant coefficients. Program is written in FORTRAN IV for batch execution and has been implemented on NOVA 1200.
Weisberg, Sanford
2013-01-01
Praise for the Third Edition ""...this is an excellent book which could easily be used as a course text...""-International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illus
Advanced statistics: linear regression, part II: multiple linear regression.
Marill, Keith A
2004-01-01
The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.
Linear regression in astronomy. I
Isobe, Takashi; Feigelson, Eric D.; Akritas, Michael G.; Babu, Gutti Jogesh
1990-01-01
Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, orthogonal regression, and 'reduced major-axis' regression. These methods have been used by various researchers in observational astronomy, most importantly in cosmic distance scale applications. Formulas for calculating the slope and intercept coefficients and their uncertainties are given for all the methods, including a new general form of the OLS variance estimates. The accuracy of the formulas was confirmed using numerical simulations. The applicability of the procedures is discussed with respect to their mathematical properties, the nature of the astronomical data under consideration, and the scientific purpose of the regression. It is found that, for problems needing symmetrical treatment of the variables, the OLS bisector performs significantly better than orthogonal or reduced major-axis regression.
Seber, George A F
2012-01-01
Concise, mathematically clear, and comprehensive treatment of the subject.* Expanded coverage of diagnostics and methods of model fitting.* Requires no specialized knowledge beyond a good grasp of matrix algebra and some acquaintance with straight-line regression and simple analysis of variance models.* More than 200 problems throughout the book plus outline solutions for the exercises.* This revision has been extensively class-tested.
Advanced statistics: linear regression, part I: simple linear regression.
Marill, Keith A
2004-01-01
Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.
Ghasemi, Jahanbakhsh; Saaidpour, Saadi
2007-01-01
A quantitative structure-property relationship (QSPR) study was performed to develop models those relate the structures of 150 drug organic compounds to their n-octanol-water partition coefficients (log P o/w ). Molecular descriptors derived solely from 3D structures of the molecular drugs. A genetic algorithm was also applied as a variable selection tool in QSPR analysis. The models were constructed using 110 molecules as training set, and predictive ability tested using 40 compounds. Modeling of log P o/w of these compounds as a function of the theoretically derived descriptors was established by multiple linear regression (MLR). Four descriptors for these compounds molecular volume (MV) (geometrical), hydrophilic-lipophilic balance (HLB) (constitutional), hydrogen bond forming ability (HB) (electronic) and polar surface area (PSA) (electrostatic) are taken as inputs for the model. The use of descriptors calculated only from molecular structure eliminates the need for experimental determination of properties for use in the correlation and allows for the estimation of log P o/w for molecules not yet synthesized. Application of the developed model to a testing set of 40 drug organic compounds demonstrates that the model is reliable with good predictive accuracy and simple formulation. The prediction results are in good agreement with the experimental value. The root mean square error of prediction (RMSEP) and square correlation coefficient (R 2 ) for MLR model were 0.22 and 0.99 for the prediction set log P o/w
Golmohammadi, Hassan
2009-11-30
A quantitative structure-property relationship (QSPR) study was performed to develop models those relate the structure of 141 organic compounds to their octanol-water partition coefficients (log P(o/w)). A genetic algorithm was applied as a variable selection tool. Modeling of log P(o/w) of these compounds as a function of theoretically derived descriptors was established by multiple linear regression (MLR), partial least squares (PLS), and artificial neural network (ANN). The best selected descriptors that appear in the models are: atomic charge weighted partial positively charged surface area (PPSA-3), fractional atomic charge weighted partial positive surface area (FPSA-3), minimum atomic partial charge (Qmin), molecular volume (MV), total dipole moment of molecule (mu), maximum antibonding contribution of a molecule orbital in the molecule (MAC), and maximum free valency of a C atom in the molecule (MFV). The result obtained showed the ability of developed artificial neural network to prediction of partition coefficients of organic compounds. Also, the results revealed the superiority of ANN over the MLR and PLS models. Copyright 2009 Wiley Periodicals, Inc.
Linear regression in astronomy. II
Feigelson, Eric D.; Babu, Gutti J.
1992-01-01
A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.
[From clinical judgment to linear regression model.
Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O
2013-01-01
When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.
Canciam, Cesar Augusto [Universidade Tecnologica Federal do Parana (UTFPR), Campus Ponta Grossa, PR (Brazil)], e-mail: canciam@utfpr.edu.br
2012-07-01
When evaluating the consumption of bio fuels, the knowledge of the density is of great importance for rectify the effect of temperature. The thermal expansion coefficient is a thermodynamic property that provides a measure of the density variation in response to temperature variation, keeping the pressure constant. This study aimed to predict the thermal expansion coefficients of ethyl bio diesels from castor beans, soybeans, sunflower seeds and Mabea fistulifera Mart. oils and of methyl bio diesels from soybeans, sunflower seeds, souari nut, cotton, coconut, castor beans and palm oils, from beef tallow, chicken fat and hydrogenated vegetable fat residual. For this purpose, there was a linear regression analysis of the density of each bio diesel a function of temperature. These data were obtained from other works. The thermal expansion coefficients for bio diesels are between 6.3729x{sup 10-4} and 1.0410x10{sup -3} degree C-1. In all the cases, the correlation coefficients were over 0.99. (author)
Kumar, Ajay; Ravi, P.M.; Guneshwar, S.L.; Rout, Sabyasachi; Mishra, Manish K.; Pulhani, Vandana; Tripathi, R.M.
2018-01-01
Numerous common methods (batch laboratory, the column laboratory, field-batch method, field modeling and K 0c method) are used frequently for determination of K d values. Recently, multiple regression models are considered as new best estimates for predicting the K d of radionuclides in the environment. It is also well known fact that the K d value is highly influenced by physico-chemical properties of sediment. Due to the significant variability in influencing parameters, the measured K d values can range over several orders of magnitude under different environmental conditions. The aim of this study is to develop a predictive model for K d values of 137 Cs and 60 Co based on the sediment properties using multiple linear regression analysis
Neutrosophic Correlation and Simple Linear Regression
A. A. Salama
2014-09-01
Full Text Available Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache. Recently, Salama et al., introduced the concept of correlation coefficient of neutrosophic data. In this paper, we introduce and study the concepts of correlation and correlation coefficient of neutrosophic data in probability spaces and study some of their properties. Also, we introduce and study the neutrosophic simple linear regression model. Possible applications to data processing are touched upon.
Quantum algorithm for linear regression
Wang, Guoming
2017-07-01
We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.
Regularized Label Relaxation Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung; Fang, Bingwu
2018-04-01
Linear regression (LR) and some of its variants have been widely used for classification problems. Most of these methods assume that during the learning phase, the training samples can be exactly transformed into a strict binary label matrix, which has too little freedom to fit the labels adequately. To address this problem, in this paper, we propose a novel regularized label relaxation LR method, which has the following notable characteristics. First, the proposed method relaxes the strict binary label matrix into a slack variable matrix by introducing a nonnegative label relaxation matrix into LR, which provides more freedom to fit the labels and simultaneously enlarges the margins between different classes as much as possible. Second, the proposed method constructs the class compactness graph based on manifold learning and uses it as the regularization item to avoid the problem of overfitting. The class compactness graph is used to ensure that the samples sharing the same labels can be kept close after they are transformed. Two different algorithms, which are, respectively, based on -norm and -norm loss functions are devised. These two algorithms have compact closed-form solutions in each iteration so that they are easily implemented. Extensive experiments show that these two algorithms outperform the state-of-the-art algorithms in terms of the classification accuracy and running time.
Nakamura, Kengo; Yasutaka, Tetsuo; Kuwatani, Tatsu; Komai, Takeshi
2017-11-01
In this study, we applied sparse multiple linear regression (SMLR) analysis to clarify the relationships between soil properties and adsorption characteristics for a range of soils across Japan and identify easily-obtained physical and chemical soil properties that could be used to predict K and n values of cadmium, lead and fluorine. A model was first constructed that can easily predict the K and n values from nine soil parameters (pH, cation exchange capacity, specific surface area, total carbon, soil organic matter from loss on ignition and water holding capacity, the ratio of sand, silt and clay). The K and n values of cadmium, lead and fluorine of 17 soil samples were used to verify the SMLR models by the root mean square error values obtained from 512 combinations of soil parameters. The SMLR analysis indicated that fluorine adsorption to soil may be associated with organic matter, whereas cadmium or lead adsorption to soil is more likely to be influenced by soil pH, IL. We found that an accurate K value can be predicted from more than three soil parameters for most soils. Approximately 65% of the predicted values were between 33 and 300% of their measured values for the K value; 76% of the predicted values were within ±30% of their measured values for the n value. Our findings suggest that adsorption properties of lead, cadmium and fluorine to soil can be predicted from the soil physical and chemical properties using the presented models. Copyright © 2017 Elsevier Ltd. All rights reserved.
Linear regression and the normality assumption.
Schmidt, Amand F; Finan, Chris
2017-12-16
Researchers often perform arbitrary outcome transformations to fulfill the normality assumption of a linear regression model. This commentary explains and illustrates that in large data settings, such transformations are often unnecessary, and worse may bias model estimates. Linear regression assumptions are illustrated using simulated data and an empirical example on the relation between time since type 2 diabetes diagnosis and glycated hemoglobin levels. Simulation results were evaluated on coverage; i.e., the number of times the 95% confidence interval included the true slope coefficient. Although outcome transformations bias point estimates, violations of the normality assumption in linear regression analyses do not. The normality assumption is necessary to unbiasedly estimate standard errors, and hence confidence intervals and P-values. However, in large sample sizes (e.g., where the number of observations per variable is >10) violations of this normality assumption often do not noticeably impact results. Contrary to this, assumptions on, the parametric model, absence of extreme observations, homoscedasticity, and independency of the errors, remain influential even in large sample size settings. Given that modern healthcare research typically includes thousands of subjects focusing on the normality assumption is often unnecessary, does not guarantee valid results, and worse may bias estimates due to the practice of outcome transformations. Copyright © 2017 Elsevier Inc. All rights reserved.
Aspects of robust linear regression
Davies, P.L.
1993-01-01
Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that $S$-estimators satisfy an exact
Comparing linear probability model coefficients across groups
Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt
2015-01-01
of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate......This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more...... these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons....
Biostatistics Series Module 6: Correlation and Linear Regression.
Hazra, Avijit; Gogtay, Nithya
2016-01-01
Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient ( r ). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P correlation coefficient can also be calculated for an idea of the correlation in the population. The value r 2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation ( y = a + bx ), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.
Granato, Gregory E.
2006-01-01
The Kendall-Theil Robust Line software (KTRLine-version 1.0) is a Visual Basic program that may be used with the Microsoft Windows operating system to calculate parameters for robust, nonparametric estimates of linear-regression coefficients between two continuous variables. The KTRLine software was developed by the U.S. Geological Survey, in cooperation with the Federal Highway Administration, for use in stochastic data modeling with local, regional, and national hydrologic data sets to develop planning-level estimates of potential effects of highway runoff on the quality of receiving waters. The Kendall-Theil robust line was selected because this robust nonparametric method is resistant to the effects of outliers and nonnormality in residuals that commonly characterize hydrologic data sets. The slope of the line is calculated as the median of all possible pairwise slopes between points. The intercept is calculated so that the line will run through the median of input data. A single-line model or a multisegment model may be specified. The program was developed to provide regression equations with an error component for stochastic data generation because nonparametric multisegment regression tools are not available with the software that is commonly used to develop regression models. The Kendall-Theil robust line is a median line and, therefore, may underestimate total mass, volume, or loads unless the error component or a bias correction factor is incorporated into the estimate. Regression statistics such as the median error, the median absolute deviation, the prediction error sum of squares, the root mean square error, the confidence interval for the slope, and the bias correction factor for median estimates are calculated by use of nonparametric methods. These statistics, however, may be used to formulate estimates of mass, volume, or total loads. The program is used to read a two- or three-column tab-delimited input file with variable names in the first row and
Determination of regression laws: Linear and nonlinear
Onishchenko, A.M.
1994-01-01
A detailed mathematical determination of regression laws is presented in the article. Particular emphasis is place on determining the laws of X j on X l to account for source nuclei decay and detector errors in nuclear physics instrumentation. Both linear and nonlinear relations are presented. Linearization of 19 functions is tabulated, including graph, relation, variable substitution, obtained linear function, and remarks. 6 refs., 1 tab
Discriminative Elastic-Net Regularized Linear Regression.
Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen
2017-03-01
In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.
Piecewise linear regression splines with hyperbolic covariates
Cologne, John B.; Sposto, Richard
1992-09-01
Consider the problem of fitting a curve to data that exhibit a multiphase linear response with smooth transitions between phases. We propose substituting hyperbolas as covariates in piecewise linear regression splines to obtain curves that are smoothly joined. The method provides an intuitive and easy way to extend the two-phase linear hyperbolic response model of Griffiths and Miller and Watts and Bacon to accommodate more than two linear segments. The resulting regression spline with hyperbolic covariates may be fit by nonlinear regression methods to estimate the degree of curvature between adjoining linear segments. The added complexity of fitting nonlinear, as opposed to linear, regression models is not great. The extra effort is particularly worthwhile when investigators are unwilling to assume that the slope of the response changes abruptly at the join points. We can also estimate the join points (the values of the abscissas where the linear segments would intersect if extrapolated) if their number and approximate locations may be presumed known. An example using data on changing age at menarche in a cohort of Japanese women illustrates the use of the method for exploratory data analysis. (author)
Removing Malmquist bias from linear regressions
Verter, Frances
1993-01-01
Malmquist bias is present in all astronomical surveys where sources are observed above an apparent brightness threshold. Those sources which can be detected at progressively larger distances are progressively more limited to the intrinsically luminous portion of the true distribution. This bias does not distort any of the measurements, but distorts the sample composition. We have developed the first treatment to correct for Malmquist bias in linear regressions of astronomical data. A demonstration of the corrected linear regression that is computed in four steps is presented.
On the Occurrence of Standardized Regression Coefficients Greater than One.
Deegan, John, Jr.
1978-01-01
It is demonstrated here that standardized regression coefficients greater than one can legitimately occur. Furthermore, the relationship between the occurrence of such coefficients and the extent of multicollinearity present among the set of predictor variables in an equation is examined. Comments on the interpretation of these coefficients are…
Finite Algorithms for Robust Linear Regression
Madsen, Kaj; Nielsen, Hans Bruun
1990-01-01
The Huber M-estimator for robust linear regression is analyzed. Newton type methods for solution of the problem are defined and analyzed, and finite convergence is proved. Numerical experiments with a large number of test problems demonstrate efficiency and indicate that this kind of approach may...
Multiple Linear Regression: A Realistic Reflector.
Nutt, A. T.; Batsell, R. R.
Examples of the use of Multiple Linear Regression (MLR) techniques are presented. This is done to show how MLR aids data processing and decision-making by providing the decision-maker with freedom in phrasing questions and by accurately reflecting the data on hand. A brief overview of the rationale underlying MLR is given, some basic definitions…
Controlling attribute effect in linear regression
Calders, Toon; Karim, Asim A.; Kamiran, Faisal; Ali, Wasif Mohammad; Zhang, Xiangliang
2013-01-01
In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.
Controlling attribute effect in linear regression
Calders, Toon
2013-12-01
In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.
Post-processing through linear regression
van Schaeybroeck, B.; Vannitsem, S.
2011-03-01
Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.
Post-processing through linear regression
B. Van Schaeybroeck
2011-03-01
Full Text Available Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS method, a new time-dependent Tikhonov regularization (TDTR method, the total least-square method, a new geometric-mean regression (GM, a recently introduced error-in-variables (EVMOS method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified.
These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise. At long lead times the regression schemes (EVMOS, TDTR which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.
Simple and multiple linear regression: sample size considerations.
Hanley, James A
2016-11-01
The suggested "two subjects per variable" (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression. This article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing "exposure" (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or "profiles." It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates. By drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres. Copyright Â© 2016 Elsevier Inc. All rights reserved.
Thermal linear expansion coefficient of structural graphites
Virgil'ev, Yu.S.
1995-01-01
The data now available on radiation induced changes of linear thermal expansion coefficients (CTE) for native structural carbon materials (SCM) irradiated with high fluences are summarized. For different types of native and foreign SCM dose dependences of CTE changes in the temperature range of 300...1600 K and at fluences up to (2...3)x10 22 n/cm 2 (E>0.18 meV) are compared. On the base of this comparison factors defined the CTE changes under neutron irradiation are revealed and the explanation of observed phenomena is offered. Large number of the factors revealed does not allowed to calculate CTE radiation induced changes. 39 refs.; 16 figs.; 5 tabs
Direction of Effects in Multiple Linear Regression Models.
Wiedermann, Wolfgang; von Eye, Alexander
2015-01-01
Previous studies analyzed asymmetric properties of the Pearson correlation coefficient using higher than second order moments. These asymmetric properties can be used to determine the direction of dependence in a linear regression setting (i.e., establish which of two variables is more likely to be on the outcome side) within the framework of cross-sectional observational data. Extant approaches are restricted to the bivariate regression case. The present contribution extends the direction of dependence methodology to a multiple linear regression setting by analyzing distributional properties of residuals of competing multiple regression models. It is shown that, under certain conditions, the third central moments of estimated regression residuals can be used to decide upon direction of effects. In addition, three different approaches for statistical inference are discussed: a combined D'Agostino normality test, a skewness difference test, and a bootstrap difference test. Type I error and power of the procedures are assessed using Monte Carlo simulations, and an empirical example is provided for illustrative purposes. In the discussion, issues concerning the quality of psychological data, possible extensions of the proposed methods to the fourth central moment of regression residuals, and potential applications are addressed.
The microcomputer scientific software series 2: general linear model--regression.
Harold M. Rauscher
1983-01-01
The general linear model regression (GLMR) program provides the microcomputer user with a sophisticated regression analysis capability. The output provides a regression ANOVA table, estimators of the regression model coefficients, their confidence intervals, confidence intervals around the predicted Y-values, residuals for plotting, a check for multicollinearity, a...
Sintering equation: determination of its coefficients by experiments - using multiple regression
Windelberg, D.
1999-01-01
Sintering is a method for volume-compression (or volume-contraction) of powdered or grained material applying high temperature (less than the melting point of the material). Maekipirtti tried to find an equation which describes the process of sintering by its main parameters sintering time, sintering temperature and volume contracting. Such equation is called a sintering equation. It also contains some coefficients which characterise the behaviour of the material during the process of sintering. These coefficients have to be determined by experiments. Here we show that some linear regressions will produce wrong coefficients, but multiple regression results in an useful sintering equation. (orig.)
Modeling maximum daily temperature using a varying coefficient regression model
Han Li; Xinwei Deng; Dong-Yum Kim; Eric P. Smith
2014-01-01
Relationships between stream water and air temperatures are often modeled using linear or nonlinear regression methods. Despite a strong relationship between water and air temperatures and a variety of models that are effective for data summarized on a weekly basis, such models did not yield consistently good predictions for summaries such as daily maximum temperature...
Linear regression crash prediction models : issues and proposed solutions.
2010-05-01
The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...
Regression Models for Predicting Force Coefficients of Aerofoils
Mohammed ABDUL AKBAR
2015-09-01
Full Text Available Renewable sources of energy are attractive and advantageous in a lot of different ways. Among the renewable energy sources, wind energy is the fastest growing type. Among wind energy converters, Vertical axis wind turbines (VAWTs have received renewed interest in the past decade due to some of the advantages they possess over their horizontal axis counterparts. VAWTs have evolved into complex 3-D shapes. A key component in predicting the output of VAWTs through analytical studies is obtaining the values of lift and drag coefficients which is a function of shape of the aerofoil, ‘angle of attack’ of wind and Reynolds’s number of flow. Sandia National Laboratories have carried out extensive experiments on aerofoils for the Reynolds number in the range of those experienced by VAWTs. The volume of experimental data thus obtained is huge. The current paper discusses three Regression analysis models developed wherein lift and drag coefficients can be found out using simple formula without having to deal with the bulk of the data. Drag coefficients and Lift coefficients were being successfully estimated by regression models with R2 values as high as 0.98.
Suppression Situations in Multiple Linear Regression
Shieh, Gwowen
2006-01-01
This article proposes alternative expressions for the two most prevailing definitions of suppression without resorting to the standardized regression modeling. The formulation provides a simple basis for the examination of their relationship. For the two-predictor regression, the author demonstrates that the previous results in the literature are…
Two Paradoxes in Linear Regression Analysis
FENG, Ge; PENG, Jing; TU, Dongke; ZHENG, Julia Z.; FENG, Changyong
2016-01-01
Summary Regression is one of the favorite tools in applied statistics. However, misuse and misinterpretation of results from regression analysis are common in biomedical research. In this paper we use statistical theory and simulation studies to clarify some paradoxes around this popular statistical method. In particular, we show that a widely used model selection procedure employed in many publications in top medical journals is wrong. Formal procedures based on solid statistical theory should be used in model selection. PMID:28638214
Fuzzy multiple linear regression: A computational approach
Juang, C. H.; Huang, X. H.; Fleming, J. W.
1992-01-01
This paper presents a new computational approach for performing fuzzy regression. In contrast to Bardossy's approach, the new approach, while dealing with fuzzy variables, closely follows the conventional regression technique. In this approach, treatment of fuzzy input is more 'computational' than 'symbolic.' The following sections first outline the formulation of the new approach, then deal with the implementation and computational scheme, and this is followed by examples to illustrate the new procedure.
On macroeconomic values investigation using fuzzy linear regression analysis
Richard Pospíšil
2017-06-01
Full Text Available The theoretical background for abstract formalization of the vague phenomenon of complex systems is the fuzzy set theory. In the paper, vague data is defined as specialized fuzzy sets - fuzzy numbers and there is described a fuzzy linear regression model as a fuzzy function with fuzzy numbers as vague parameters. To identify the fuzzy coefficients of the model, the genetic algorithm is used. The linear approximation of the vague function together with its possibility area is analytically and graphically expressed. A suitable application is performed in the tasks of the time series fuzzy regression analysis. The time-trend and seasonal cycles including their possibility areas are calculated and expressed. The examples are presented from the economy field, namely the time-development of unemployment, agricultural production and construction respectively between 2009 and 2011 in the Czech Republic. The results are shown in the form of the fuzzy regression models of variables of time series. For the period 2009-2011, the analysis assumptions about seasonal behaviour of variables and the relationship between them were confirmed; in 2010, the system behaved fuzzier and the relationships between the variables were vaguer, that has a lot of causes, from the different elasticity of demand, through state interventions to globalization and transnational impacts.
Yoneoka, Daisuke; Henmi, Masayuki
2017-11-30
Recently, the number of clinical prediction models sharing the same regression task has increased in the medical literature. However, evidence synthesis methodologies that use the results of these regression models have not been sufficiently studied, particularly in meta-analysis settings where only regression coefficients are available. One of the difficulties lies in the differences between the categorization schemes of continuous covariates across different studies. In general, categorization methods using cutoff values are study specific across available models, even if they focus on the same covariates of interest. Differences in the categorization of covariates could lead to serious bias in the estimated regression coefficients and thus in subsequent syntheses. To tackle this issue, we developed synthesis methods for linear regression models with different categorization schemes of covariates. A 2-step approach to aggregate the regression coefficient estimates is proposed. The first step is to estimate the joint distribution of covariates by introducing a latent sampling distribution, which uses one set of individual participant data to estimate the marginal distribution of covariates with categorization. The second step is to use a nonlinear mixed-effects model with correction terms for the bias due to categorization to estimate the overall regression coefficients. Especially in terms of precision, numerical simulations show that our approach outperforms conventional methods, which only use studies with common covariates or ignore the differences between categorization schemes. The method developed in this study is also applied to a series of WHO epidemiologic studies on white blood cell counts. Copyright © 2017 John Wiley & Sons, Ltd.
Linear Regression Based Real-Time Filtering
Misel Batmend
2013-01-01
Full Text Available This paper introduces real time filtering method based on linear least squares fitted line. Method can be used in case that a filtered signal is linear. This constraint narrows a band of potential applications. Advantage over Kalman filter is that it is computationally less expensive. The paper further deals with application of introduced method on filtering data used to evaluate a position of engraved material with respect to engraving machine. The filter was implemented to the CNC engraving machine control system. Experiments showing its performance are included.
Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan
2017-01-01
This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second
New Inference Procedures for Semiparametric Varying-Coefficient Partially Linear Cox Models
Yunbei Ma
2014-01-01
Full Text Available In biomedical research, one major objective is to identify risk factors and study their risk impacts, as this identification can help clinicians to both properly make a decision and increase efficiency of treatments and resource allocation. A two-step penalized-based procedure is proposed to select linear regression coefficients for linear components and to identify significant nonparametric varying-coefficient functions for semiparametric varying-coefficient partially linear Cox models. It is shown that the penalized-based resulting estimators of the linear regression coefficients are asymptotically normal and have oracle properties, and the resulting estimators of the varying-coefficient functions have optimal convergence rates. A simulation study and an empirical example are presented for illustration.
Augmenting Data with Published Results in Bayesian Linear Regression
de Leeuw, Christiaan; Klugkist, Irene
2012-01-01
In most research, linear regression analyses are performed without taking into account published results (i.e., reported summary statistics) of similar previous studies. Although the prior density in Bayesian linear regression could accommodate such prior knowledge, formal models for doing so are absent from the literature. The goal of this…
A test for the parameters of multiple linear regression models ...
A test for the parameters of multiple linear regression models is developed for conducting tests simultaneously on all the parameters of multiple linear regression models. The test is robust relative to the assumptions of homogeneity of variances and absence of serial correlation of the classical F-test. Under certain null and ...
Who Will Win?: Predicting the Presidential Election Using Linear Regression
Lamb, John H.
2007-01-01
This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…
Overcoming multicollinearity in multiple regression using correlation coefficient
Zainodin, H. J.; Yap, S. J.
2013-09-01
Multicollinearity happens when there are high correlations among independent variables. In this case, it would be difficult to distinguish between the contributions of these independent variables to that of the dependent variable as they may compete to explain much of the similar variance. Besides, the problem of multicollinearity also violates the assumption of multiple regression: that there is no collinearity among the possible independent variables. Thus, an alternative approach is introduced in overcoming the multicollinearity problem in achieving a well represented model eventually. This approach is accomplished by removing the multicollinearity source variables on the basis of the correlation coefficient values based on full correlation matrix. Using the full correlation matrix can facilitate the implementation of Excel function in removing the multicollinearity source variables. It is found that this procedure is easier and time-saving especially when dealing with greater number of independent variables in a model and a large number of all possible models. Hence, in this paper detailed insight of the procedure is shown, compared and implemented.
An improved multiple linear regression and data analysis computer program package
Sidik, S. M.
1972-01-01
NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.
Implicit collinearity effect in linear regression: Application to basal ...
Collinearity of predictor variables is a severe problem in the least square regression analysis. It contributes to the instability of regression coefficients and leads to a wrong prediction accuracy. Despite these problems, studies are conducted with a large number of observed and derived variables linked with a response ...
Use of probabilistic weights to enhance linear regression myoelectric control.
Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J
2015-12-01
Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts' law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p linear regression control. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.
Distributed Monitoring of the R2 Statistic for Linear Regression
National Aeronautics and Space Administration — The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and...
Identification of Influential Points in a Linear Regression Model
Jan Grosz
2011-03-01
Full Text Available The article deals with the detection and identification of influential points in the linear regression model. Three methods of detection of outliers and leverage points are described. These procedures can also be used for one-sample (independentdatasets. This paper briefly describes theoretical aspects of several robust methods as well. Robust statistics is a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. A simulation model of the simple linear regression is presented.
Learning a Nonnegative Sparse Graph for Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung
2015-09-01
Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.
Teaching the Concept of Breakdown Point in Simple Linear Regression.
Chan, Wai-Sum
2001-01-01
Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…
Testing hypotheses for differences between linear regression lines
Stanley J. Zarnoch
2009-01-01
Five hypotheses are identified for testing differences between simple linear regression lines. The distinctions between these hypotheses are based on a priori assumptions and illustrated with full and reduced models. The contrast approach is presented as an easy and complete method for testing for overall differences between the regressions and for making pairwise...
Evaluation of Linear Regression Simultaneous Myoelectric Control Using Intramuscular EMG.
Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J
2016-04-01
The objective of this study was to evaluate the ability of linear regression models to decode patterns of muscle coactivation from intramuscular electromyogram (EMG) and provide simultaneous myoelectric control of a virtual 3-DOF wrist/hand system. Performance was compared to the simultaneous control of conventional myoelectric prosthesis methods using intramuscular EMG (parallel dual-site control)-an approach that requires users to independently modulate individual muscles in the residual limb, which can be challenging for amputees. Linear regression control was evaluated in eight able-bodied subjects during a virtual Fitts' law task and was compared to performance of eight subjects using parallel dual-site control. An offline analysis also evaluated how different types of training data affected prediction accuracy of linear regression control. The two control systems demonstrated similar overall performance; however, the linear regression method demonstrated improved performance for targets requiring use of all three DOFs, whereas parallel dual-site control demonstrated improved performance for targets that required use of only one DOF. Subjects using linear regression control could more easily activate multiple DOFs simultaneously, but often experienced unintended movements when trying to isolate individual DOFs. Offline analyses also suggested that the method used to train linear regression systems may influence controllability. Linear regression myoelectric control using intramuscular EMG provided an alternative to parallel dual-site control for 3-DOF simultaneous control at the wrist and hand. The two methods demonstrated different strengths in controllability, highlighting the tradeoff between providing simultaneous control and the ability to isolate individual DOFs when desired.
Interpreting Bivariate Regression Coefficients: Going beyond the Average
Halcoussis, Dennis; Phillips, G. Michael
2010-01-01
Statistics, econometrics, investment analysis, and data analysis classes often review the calculation of several types of averages, including the arithmetic mean, geometric mean, harmonic mean, and various weighted averages. This note shows how each of these can be computed using a basic regression framework. By recognizing when a regression model…
Estimating monotonic rates from biological data using local linear regression.
Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R
2017-03-01
Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.
KELEŞ, Taliha; ALTUN, Murat
2016-01-01
Regression analysis is a statistical technique for investigating and modeling the relationship between variables. The purpose of this study was the trivial presentation of the equation for orthogonal regression (OR) and the comparison of classical linear regression (CLR) and OR techniques with respect to the sum of squared perpendicular distances. For that purpose, the analyses were shown by an example. It was found that the sum of squared perpendicular distances of OR is smaller. Thus, it wa...
Use of probabilistic weights to enhance linear regression myoelectric control
Smith, Lauren H.; Kuiken, Todd A.; Hargrove, Levi J.
2015-12-01
Objective. Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Approach. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts’ law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Main results. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p < 0.05) by preventing extraneous movement at additional DOFs. Similar results were seen in experiments with two transradial amputees. Though goodness-of-fit evaluations suggested that the EMG feature distributions showed some deviations from the Gaussian, equal-covariance assumptions used in this experiment, the assumptions were sufficiently met to provide improved performance compared to linear regression control. Significance. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.
The number of subjects per variable required in linear regression analyses.
Austin, Peter C; Steyerberg, Ewout W
2015-06-01
To determine the number of independent variables that can be included in a linear regression model. We used a series of Monte Carlo simulations to examine the impact of the number of subjects per variable (SPV) on the accuracy of estimated regression coefficients and standard errors, on the empirical coverage of estimated confidence intervals, and on the accuracy of the estimated R(2) of the fitted model. A minimum of approximately two SPV tended to result in estimation of regression coefficients with relative bias of less than 10%. Furthermore, with this minimum number of SPV, the standard errors of the regression coefficients were accurately estimated and estimated confidence intervals had approximately the advertised coverage rates. A much higher number of SPV were necessary to minimize bias in estimating the model R(2), although adjusted R(2) estimates behaved well. The bias in estimating the model R(2) statistic was inversely proportional to the magnitude of the proportion of variation explained by the population regression model. Linear regression models require only two SPV for adequate estimation of regression coefficients, standard errors, and confidence intervals. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
Measurement of linear attenuation coefficient of different materials
Ali, M. M.
2013-07-01
In this research we study the linear attenuation coefficient from the materials concrete, brick, mixture concrete and iron. In the secondary standard dosimetry laboratory in Atomic Energy from different distance by use Cs-137 sours, chamber farmer 2675 A-600 cc-S/N 0511, and electrometer 2670 A-S/N 114. Found the value of linear attenuation coefficient of concert in the range 0.167 cm -1 , the brick in the range 0.063 -1 and mixture concrete and iron in the range 0.253cm -1 .(Author)
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander
2014-01-06
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander; Matthies, Hermann G.; Pojonk, Oliver; Rosic, Bojana V.; Zander, Elmar
2014-01-01
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Analysis of interactive fixed effects dynamic linear panel regression with measurement error
Nayoung Lee; Hyungsik Roger Moon; Martin Weidner
2011-01-01
This paper studies a simple dynamic panel linear regression model with interactive fixed effects in which the variable of interest is measured with error. To estimate the dynamic coefficient, we consider the least-squares minimum distance (LS-MD) estimation method.
Calculation of U, Ra, Th and K contents in uranium ore by multiple linear regression method
Lin Chao; Chen Yingqiang; Zhang Qingwen; Tan Fuwen; Peng Guanghui
1991-01-01
A multiple linear regression method was used to compute γ spectra of uranium ore samples and to calculate contents of U, Ra, Th, and K. In comparison with the inverse matrix method, its advantage is that no standard samples of pure U, Ra, Th and K are needed for obtaining response coefficients
Linear regression methods a ccording to objective functions
Yasemin Sisman; Sebahattin Bektas
2012-01-01
The aim of the study is to explain the parameter estimation methods and the regression analysis. The simple linear regressionmethods grouped according to the objective function are introduced. The numerical solution is achieved for the simple linear regressionmethods according to objective function of Least Squares and theLeast Absolute Value adjustment methods. The success of the appliedmethods is analyzed using their objective function values.
Bias in regression coefficient estimates upon different treatments of ...
MS and PW consistently overestimated the population parameter. EM and RI, on the other hand, tended to consistently underestimate the population parameter under non-monotonic pattern. Keywords: Missing data, bias, regression, percent missing, non-normality, missing pattern > East African Journal of Statistics Vol.
Overall mass-transfer coefficients in non-linear chromatography
Mollerup, Jørgen; Hansen, Ernst
1998-01-01
In case of mass transfer where concentration differences in both phases must be taken into account, one may define an over-all mass-transfer coefficient basd on the apparent over-all concentration difference. If the equilibrium relationship is linear, i.e. in cases where a Henry´s law relationshi...
General guidelines solution for linear programming with fuzzy coefficients
Sergio Gerardo de los Cobos Silva
2013-08-01
Full Text Available This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp. This work presents some examples based on [1].
Optimal choice of basis functions in the linear regression analysis
Khotinskij, A.M.
1988-01-01
Problem of optimal choice of basis functions in the linear regression analysis is investigated. Step algorithm with estimation of its efficiency, which holds true at finite number of measurements, is suggested. Conditions, providing the probability of correct choice close to 1 are formulated. Application of the step algorithm to analysis of decay curves is substantiated. 8 refs
Common pitfalls in statistical analysis: Linear regression analysis
Rakesh Aggarwal
2017-01-01
Full Text Available In a previous article in this series, we explained correlation analysis which describes the strength of relationship between two continuous variables. In this article, we deal with linear regression analysis which predicts the value of one continuous variable from another. We also discuss the assumptions and pitfalls associated with this analysis.
How Robust Is Linear Regression with Dummy Variables?
Blankmeyer, Eric
2006-01-01
Researchers in education and the social sciences make extensive use of linear regression models in which the dependent variable is continuous-valued while the explanatory variables are a combination of continuous-valued regressors and dummy variables. The dummies partition the sample into groups, some of which may contain only a few observations.…
On the null distribution of Bayes factors in linear regression
We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...
Fitting program for linear regressions according to Mahon (1996)
2018-01-09
This program takes the users' Input data and fits a linear regression to it using the prescription presented by Mahon (1996). Compared to the commonly used York fit, this method has the correct prescription for measurement error propagation. This software should facilitate the proper fitting of measurements with a simple Interface.
Data Transformations for Inference with Linear Regression: Clarifications and Recommendations
Pek, Jolynn; Wong, Octavia; Wong, C. M.
2017-01-01
Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…
Coefficient of linear attenuation of beer for γ rays of 662 keV
Ortiz A, M. D.; Cano S, D.; Vega C, H. R.
2017-10-01
The coefficient of linear attenuation of the beer was determined by means of a transmission experiment with a source of Cs 137 and a gamma ray spectrometer with a NaI(Tl) detector of 7.62 cm in diameter and 7.62 cm in height, using narrow geometry. The pulse height spectrum was accumulated for 1 minute of live time, 7 beer thicknesses (0.6 cm) were used. By means of linear regression by weighted squares we determined the linear attenuation coefficient whose value was μ = 0.0843 ± 0.0007 cm -1 . The coefficient of linear attenuation of water is 2.2% times greater than that of beer and to the geometry of the experimental arrangement. (Author)
Linear regression and sensitivity analysis in nuclear reactor design
Kumar, Akansha; Tsvetkov, Pavel V.; McClarren, Ryan G.
2015-01-01
Highlights: • Presented a benchmark for the applicability of linear regression to complex systems. • Applied linear regression to a nuclear reactor power system. • Performed neutronics, thermal–hydraulics, and energy conversion using Brayton’s cycle for the design of a GCFBR. • Performed detailed sensitivity analysis to a set of parameters in a nuclear reactor power system. • Modeled and developed reactor design using MCNP, regression using R, and thermal–hydraulics in Java. - Abstract: The paper presents a general strategy applicable for sensitivity analysis (SA), and uncertainity quantification analysis (UA) of parameters related to a nuclear reactor design. This work also validates the use of linear regression (LR) for predictive analysis in a nuclear reactor design. The analysis helps to determine the parameters on which a LR model can be fit for predictive analysis. For those parameters, a regression surface is created based on trial data and predictions are made using this surface. A general strategy of SA to determine and identify the influential parameters those affect the operation of the reactor is mentioned. Identification of design parameters and validation of linearity assumption for the application of LR of reactor design based on a set of tests is performed. The testing methods used to determine the behavior of the parameters can be used as a general strategy for UA, and SA of nuclear reactor models, and thermal hydraulics calculations. A design of a gas cooled fast breeder reactor (GCFBR), with thermal–hydraulics, and energy transfer has been used for the demonstration of this method. MCNP6 is used to simulate the GCFBR design, and perform the necessary criticality calculations. Java is used to build and run input samples, and to extract data from the output files of MCNP6, and R is used to perform regression analysis and other multivariate variance, and analysis of the collinearity of data
SPLINE LINEAR REGRESSION USED FOR EVALUATING FINANCIAL ASSETS 1
Liviu GEAMBAŞU
2010-12-01
Full Text Available One of the most important preoccupations of financial markets participants was and still is the problem of determining more precise the trend of financial assets prices. For solving this problem there were written many scientific papers and were developed many mathematical and statistical models in order to better determine the financial assets price trend. If until recently the simple linear models were largely used due to their facile utilization, the financial crises that affected the world economy starting with 2008 highlight the necessity of adapting the mathematical models to variation of economy. A simple to use model but adapted to economic life realities is the spline linear regression. This type of regression keeps the continuity of regression function, but split the studied data in intervals with homogenous characteristics. The characteristics of each interval are highlighted and also the evolution of market over all the intervals, resulting reduced standard errors. The first objective of the article is the theoretical presentation of the spline linear regression, also referring to scientific national and international papers related to this subject. The second objective is applying the theoretical model to data from the Bucharest Stock Exchange
Implementing fuzzy polynomial interpolation (FPI and fuzzy linear regression (LFR
Maria Cristina Floreno
1996-05-01
Full Text Available This paper presents some preliminary results arising within a general framework concerning the development of software tools for fuzzy arithmetic. The program is in a preliminary stage. What has been already implemented consists of a set of routines for elementary operations, optimized functions evaluation, interpolation and regression. Some of these have been applied to real problems.This paper describes a prototype of a library in C++ for polynomial interpolation of fuzzifying functions, a set of routines in FORTRAN for fuzzy linear regression and a program with graphical user interface allowing the use of such routines.
Stochastic development regression on non-linear manifolds
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...
Distributing Correlation Coefficients of Linear Structure-Activity/Property Models
Sorana D. BOLBOACA
2011-12-01
Full Text Available Quantitative structure-activity/property relationships are mathematical relationships linking chemical structure and activity/property in a quantitative manner. These in silico approaches are frequently used to reduce animal testing and risk-assessment, as well as to increase time- and cost-effectiveness in characterization and identification of active compounds. The aim of our study was to investigate the pattern of correlation coefficients distribution associated to simple linear relationships linking the compounds structure with their activities. A set of the most common ordnance compounds found at naval facilities with a limited data set with a range of toxicities on aquatic ecosystem and a set of seven properties was studied. Statistically significant models were selected and investigated. The probability density function of the correlation coefficients was investigated using a series of possible continuous distribution laws. Almost 48% of the correlation coefficients proved fit Beta distribution, 40% fit Generalized Pareto distribution, and 12% fit Pert distribution.
Midgley, S M
2004-01-21
A novel parameterization of x-ray interaction cross-sections is developed, and employed to describe the x-ray linear attenuation coefficient and mass energy absorption coefficient for both elements and mixtures. The new parameterization scheme addresses the Z-dependence of elemental cross-sections (per electron) using a simple function of atomic number, Z. This obviates the need for a complicated mathematical formalism. Energy dependent coefficients describe the Z-direction curvature of the cross-sections. The composition dependent quantities are the electron density and statistical moments describing the elemental distribution. We show that it is possible to describe elemental cross-sections for the entire periodic table and at energies above the K-edge (from 6 keV to 125 MeV), with an accuracy of better than 2% using a parameterization containing not more than five coefficients. For the biologically important elements 1 coefficients. At higher energies, the parameterization uses fewer coefficients with only two coefficients needed at megavoltage energies.
Computer software for linear and nonlinear regression in organic NMR
Canto, Eduardo Leite do; Rittner, Roberto
1991-01-01
Calculation involving two variable linear regressions, require specific procedures generally not familiar to chemist. For attending the necessity of fast and efficient handling of NMR data, a self explained and Pc portable software has been developed, which allows user to produce and use diskette recorded tables, containing chemical shift or any other substituent physical-chemical measurements and constants (σ T , σ o R , E s , ...)
Multicollinearity in applied economics research and the Bayesian linear regression
EISENSTAT, Eric
2016-01-01
This article revises the popular issue of collinearity amongst explanatory variables in the context of a multiple linear regression analysis, particularly in empirical studies within social science related fields. Some important interpretations and explanations are highlighted from the econometrics literature with respect to the effects of multicollinearity on statistical inference, as well as the general shortcomings of the once fervent search for methods intended to detect and mitigate thes...
Faraway, Julian J
2005-01-01
Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway''s critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author''s treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the ...
Establishment of regression dependences. Linear and nonlinear dependences
Onishchenko, A.M.
1994-01-01
The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab
Return-Volatility Relationship: Insights from Linear and Non-Linear Quantile Regression
D.E. Allen (David); A.K. Singh (Abhay); R.J. Powell (Robert); M.J. McAleer (Michael); J. Taylor (James); L. Thomas (Lyn)
2013-01-01
textabstractThe purpose of this paper is to examine the asymmetric relationship between price and implied volatility and the associated extreme quantile dependence using linear and non linear quantile regression approach. Our goal in this paper is to demonstrate that the relationship between the
BRGLM, Interactive Linear Regression Analysis by Least Square Fit
Ringland, J.T.; Bohrer, R.E.; Sherman, M.E.
1985-01-01
1 - Description of program or function: BRGLM is an interactive program written to fit general linear regression models by least squares and to provide a variety of statistical diagnostic information about the fit. Stepwise and all-subsets regression can be carried out also. There are facilities for interactive data management (e.g. setting missing value flags, data transformations) and tools for constructing design matrices for the more commonly-used models such as factorials, cubic Splines, and auto-regressions. 2 - Method of solution: The least squares computations are based on the orthogonal (QR) decomposition of the design matrix obtained using the modified Gram-Schmidt algorithm. 3 - Restrictions on the complexity of the problem: The current release of BRGLM allows maxima of 1000 observations, 99 variables, and 3000 words of main memory workspace. For a problem with N observations and P variables, the number of words of main memory storage required is MAX(N*(P+6), N*P+P*P+3*N, and 3*P*P+6*N). Any linear model may be fit although the in-memory workspace will have to be increased for larger problems
Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?
Stinchcombe, John R; Agrawal, Aneil F; Hohenlohe, Paul A; Arnold, Stevan J; Blows, Mark W
2008-09-01
The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.
Linear regression metamodeling as a tool to summarize and present simulation model results.
Jalal, Hawre; Dowd, Bryan; Sainfort, François; Kuntz, Karen M
2013-10-01
Modelers lack a tool to systematically and clearly present complex model results, including those from sensitivity analyses. The objective was to propose linear regression metamodeling as a tool to increase transparency of decision analytic models and better communicate their results. We used a simplified cancer cure model to demonstrate our approach. The model computed the lifetime cost and benefit of 3 treatment options for cancer patients. We simulated 10,000 cohorts in a probabilistic sensitivity analysis (PSA) and regressed the model outcomes on the standardized input parameter values in a set of regression analyses. We used the regression coefficients to describe measures of sensitivity analyses, including threshold and parameter sensitivity analyses. We also compared the results of the PSA to deterministic full-factorial and one-factor-at-a-time designs. The regression intercept represented the estimated base-case outcome, and the other coefficients described the relative parameter uncertainty in the model. We defined simple relationships that compute the average and incremental net benefit of each intervention. Metamodeling produced outputs similar to traditional deterministic 1-way or 2-way sensitivity analyses but was more reliable since it used all parameter values. Linear regression metamodeling is a simple, yet powerful, tool that can assist modelers in communicating model characteristics and sensitivity analyses.
Smith, Paul F; Ganesh, Siva; Liu, Ping
2013-10-30
Regression is a common statistical tool for prediction in neuroscience. However, linear regression is by far the most common form of regression used, with regression trees receiving comparatively little attention. In this study, the results of conventional multiple linear regression (MLR) were compared with those of random forest regression (RFR), in the prediction of the concentrations of 9 neurochemicals in the vestibular nucleus complex and cerebellum that are part of the l-arginine biochemical pathway (agmatine, putrescine, spermidine, spermine, l-arginine, l-ornithine, l-citrulline, glutamate and γ-aminobutyric acid (GABA)). The R(2) values for the MLRs were higher than the proportion of variance explained values for the RFRs: 6/9 of them were ≥ 0.70 compared to 4/9 for RFRs. Even the variables that had the lowest R(2) values for the MLRs, e.g. ornithine (0.50) and glutamate (0.61), had much lower proportion of variance explained values for the RFRs (0.27 and 0.49, respectively). The RSE values for the MLRs were lower than those for the RFRs in all but two cases. In general, MLRs seemed to be superior to the RFRs in terms of predictive value and error. In the case of this data set, MLR appeared to be superior to RFR in terms of its explanatory value and error. This result suggests that MLR may have advantages over RFR for prediction in neuroscience with this kind of data set, but that RFR can still have good predictive value in some cases. Copyright © 2013 Elsevier B.V. All rights reserved.
Linear thermal expansion coefficient measurement technology in hot cell
Park, Dae Gyu; Choo, Yong Sun; Ahn, Sang Bok; Hong, Kwon Pyo; Lee, K. S.
1998-06-01
To establish linear thermal expansion coefficient measurement technology in hot cell, we reviewed and evaluated various measuring technology by paper and these were compared with the data produced with pre-installed dilatometer in hot cell. Detailed contents are as follows; - The theory of test. - Review of characteristics for various measurement technology and compatibility with hot cell. - Review of standard testing regulations(ASTM). - System calibration of pre-installed dilatometer. - Performance test of pre-installed dilatometer. (author). 12 refs., 15 tabs., 8 figs
Cruz, Antonio M; Barr, Cameron; Puñales-Pozo, Elsa
2008-01-01
This research's main goals were to build a predictor for a turnaround time (TAT) indicator for estimating its values and use a numerical clustering technique for finding possible causes of undesirable TAT values. The following stages were used: domain understanding, data characterisation and sample reduction and insight characterisation. Building the TAT indicator multiple linear regression predictor and clustering techniques were used for improving corrective maintenance task efficiency in a clinical engineering department (CED). The indicator being studied was turnaround time (TAT). Multiple linear regression was used for building a predictive TAT value model. The variables contributing to such model were clinical engineering department response time (CE(rt), 0.415 positive coefficient), stock service response time (Stock(rt), 0.734 positive coefficient), priority level (0.21 positive coefficient) and service time (0.06 positive coefficient). The regression process showed heavy reliance on Stock(rt), CE(rt) and priority, in that order. Clustering techniques revealed the main causes of high TAT values. This examination has provided a means for analysing current technical service quality and effectiveness. In doing so, it has demonstrated a process for identifying areas and methods of improvement and a model against which to analyse these methods' effectiveness.
A note on the use of multiple linear regression in molecular ecology.
Frasier, Timothy R
2016-03-01
Multiple linear regression analyses (also often referred to as generalized linear models--GLMs, or generalized linear mixed models--GLMMs) are widely used in the analysis of data in molecular ecology, often to assess the relative effects of genetic characteristics on individual fitness or traits, or how environmental characteristics influence patterns of genetic differentiation. However, the coefficients resulting from multiple regression analyses are sometimes misinterpreted, which can lead to incorrect interpretations and conclusions within individual studies, and can propagate to wider-spread errors in the general understanding of a topic. The primary issue revolves around the interpretation of coefficients for independent variables when interaction terms are also included in the analyses. In this scenario, the coefficients associated with each independent variable are often interpreted as the independent effect of each predictor variable on the predicted variable. However, this interpretation is incorrect. The correct interpretation is that these coefficients represent the effect of each predictor variable on the predicted variable when all other predictor variables are zero. This difference may sound subtle, but the ramifications cannot be overstated. Here, my goals are to raise awareness of this issue, to demonstrate and emphasize the problems that can result and to provide alternative approaches for obtaining the desired information. © 2015 John Wiley & Sons Ltd.
Local energy decay for linear wave equations with variable coefficients
Ikehata, Ryo
2005-06-01
A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].
Relative Importance for Linear Regression in R: The Package relaimpo
Ulrike Gromping
2006-09-01
Full Text Available Relative importance is a topic that has seen a lot of interest in recent years, particularly in applied work. The R package relaimpo implements six different metrics for assessing relative importance of regressors in the linear model, two of which are recommended - averaging over orderings of regressors and a newly proposed metric (Feldman 2005 called pmvd. Apart from delivering the metrics themselves, relaimpo also provides (exploratory bootstrap confidence intervals. This paper offers a brief tutorial introduction to the package. The methods and relaimpo’s functionality are illustrated using the data set swiss that is generally available in R. The paper targets readers who have a basic understanding of multiple linear regression. For the background of more advanced aspects, references are provided.
Stochastic development regression on non-linear manifolds
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....
Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William
2016-01-01
,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation. Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.
Gusriani, N.; Firdaniza
2018-03-01
The existence of outliers on multiple linear regression analysis causes the Gaussian assumption to be unfulfilled. If the Least Square method is forcedly used on these data, it will produce a model that cannot represent most data. For that, we need a robust regression method against outliers. This paper will compare the Minimum Covariance Determinant (MCD) method and the TELBS method on secondary data on the productivity of phytoplankton, which contains outliers. Based on the robust determinant coefficient value, MCD method produces a better model compared to TELBS method.
Robust linear registration of CT images using random regression forests
Konukoglu, Ender; Criminisi, Antonio; Pathak, Sayan; Robertson, Duncan; White, Steve; Haynor, David; Siddiqui, Khan
2011-03-01
Global linear registration is a necessary first step for many different tasks in medical image analysis. Comparing longitudinal studies1, cross-modality fusion2, and many other applications depend heavily on the success of the automatic registration. The robustness and efficiency of this step is crucial as it affects all subsequent operations. Most common techniques cast the linear registration problem as the minimization of a global energy function based on the image intensities. Although these algorithms have proved useful, their robustness in fully automated scenarios is still an open question. In fact, the optimization step often gets caught in local minima yielding unsatisfactory results. Recent algorithms constrain the space of registration parameters by exploiting implicit or explicit organ segmentations, thus increasing robustness4,5. In this work we propose a novel robust algorithm for automatic global linear image registration. Our method uses random regression forests to estimate posterior probability distributions for the locations of anatomical structures - represented as axis aligned bounding boxes6. These posterior distributions are later integrated in a global linear registration algorithm. The biggest advantage of our algorithm is that it does not require pre-defined segmentations or regions. Yet it yields robust registration results. We compare the robustness of our algorithm with that of the state of the art Elastix toolbox7. Validation is performed via 1464 pair-wise registrations in a database of very diverse 3D CT images. We show that our method decreases the "failure" rate of the global linear registration from 12.5% (Elastix) to only 1.9%.
Qiutong Jin
2016-06-01
Full Text Available Estimating the spatial distribution of precipitation is an important and challenging task in hydrology, climatology, ecology, and environmental science. In order to generate a highly accurate distribution map of average annual precipitation for the Loess Plateau in China, multiple linear regression Kriging (MLRK and geographically weighted regression Kriging (GWRK methods were employed using precipitation data from the period 1980–2010 from 435 meteorological stations. The predictors in regression Kriging were selected by stepwise regression analysis from many auxiliary environmental factors, such as elevation (DEM, normalized difference vegetation index (NDVI, solar radiation, slope, and aspect. All predictor distribution maps had a 500 m spatial resolution. Validation precipitation data from 130 hydrometeorological stations were used to assess the prediction accuracies of the MLRK and GWRK approaches. Results showed that both prediction maps with a 500 m spatial resolution interpolated by MLRK and GWRK had a high accuracy and captured detailed spatial distribution data; however, MLRK produced a lower prediction error and a higher variance explanation than GWRK, although the differences were small, in contrast to conclusions from similar studies.
A primer for biomedical scientists on how to execute model II linear regression analysis.
Ludbrook, John
2012-04-01
1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions. © 2011 The Author. Clinical and Experimental Pharmacology and Physiology. © 2011 Blackwell Publishing Asia Pty Ltd.
Laurens, L M L; Wolfrum, E J
2013-12-18
One of the challenges associated with microalgal biomass characterization and the comparison of microalgal strains and conversion processes is the rapid determination of the composition of algae. We have developed and applied a high-throughput screening technology based on near-infrared (NIR) spectroscopy for the rapid and accurate determination of algal biomass composition. We show that NIR spectroscopy can accurately predict the full composition using multivariate linear regression analysis of varying lipid, protein, and carbohydrate content of algal biomass samples from three strains. We also demonstrate a high quality of predictions of an independent validation set. A high-throughput 96-well configuration for spectroscopy gives equally good prediction relative to a ring-cup configuration, and thus, spectra can be obtained from as little as 10-20 mg of material. We found that lipids exhibit a dominant, distinct, and unique fingerprint in the NIR spectrum that allows for the use of single and multiple linear regression of respective wavelengths for the prediction of the biomass lipid content. This is not the case for carbohydrate and protein content, and thus, the use of multivariate statistical modeling approaches remains necessary.
Convergence diagnostics for Eigenvalue problems with linear regression model
Shi, Bo; Petrovic, Bojan
2011-01-01
Although the Monte Carlo method has been extensively used for criticality/Eigenvalue problems, a reliable, robust, and efficient convergence diagnostics method is still desired. Most methods are based on integral parameters (multiplication factor, entropy) and either condense the local distribution information into a single value (e.g., entropy) or even disregard it. We propose to employ the detailed cycle-by-cycle local flux evolution obtained by using mesh tally mechanism to assess the source and flux convergence. By applying a linear regression model to each individual mesh in a mesh tally for convergence diagnostics, a global convergence criterion can be obtained. We exemplify this method on two problems and obtain promising diagnostics results. (author)
Li, Yanming; Nan, Bin; Zhu, Ji
2015-06-01
We propose a multivariate sparse group lasso variable selection and estimation method for data with high-dimensional predictors as well as high-dimensional response variables. The method is carried out through a penalized multivariate multiple linear regression model with an arbitrary group structure for the regression coefficient matrix. It suits many biology studies well in detecting associations between multiple traits and multiple predictors, with each trait and each predictor embedded in some biological functional groups such as genes, pathways or brain regions. The method is able to effectively remove unimportant groups as well as unimportant individual coefficients within important groups, particularly for large p small n problems, and is flexible in handling various complex group structures such as overlapping or nested or multilevel hierarchical structures. The method is evaluated through extensive simulations with comparisons to the conventional lasso and group lasso methods, and is applied to an eQTL association study. © 2015, The International Biometric Society.
Regressão linear geograficamente ponderada em ambiente SIG
Luís Eduardo Ximenes Carvalho
2009-10-01
Full Text Available
Este artigo aborda considerações teóricas e resultados da implementação em ambiente SIG de um modelo confirmatório de estatística espacial — regressão linear geograficamente ponderada (RGP — não disponível em ambiente livre. Os aspectos teóricos deste modelo local de regressão espacial foram amplamente discutidos em virtude da escassa bibliografia existente. O modelo RGP foi implementado na linguagem de programação GISDK do SIG-T TransCAD, utilizando compreensivamente as ferramentas de manipulação, tratamento georreferenciado dos dados e rotinas de análise espacial disponibilizadas em plataformas SIG. Ao final, espera-se ter desenvolvido, ainda que de maneira parcial, uma importante ferramenta que contribuirá para a compreensão e refinamento da modelagem de fenômenos geográficos tão amplamente analisados em estudos de Planejamento de Transportes.
Modeling Pan Evaporation for Kuwait by Multiple Linear Regression
Almedeij, Jaber
2012-01-01
Evaporation is an important parameter for many projects related to hydrology and water resources systems. This paper constitutes the first study conducted in Kuwait to obtain empirical relations for the estimation of daily and monthly pan evaporation as functions of available meteorological data of temperature, relative humidity, and wind speed. The data used here for the modeling are daily measurements of substantial continuity coverage, within a period of 17 years between January 1993 and December 2009, which can be considered representative of the desert climate of the urban zone of the country. Multiple linear regression technique is used with a procedure of variable selection for fitting the best model forms. The correlations of evaporation with temperature and relative humidity are also transformed in order to linearize the existing curvilinear patterns of the data by using power and exponential functions, respectively. The evaporation models suggested with the best variable combinations were shown to produce results that are in a reasonable agreement with observation values. PMID:23226984
Improvement of Storm Forecasts Using Gridded Bayesian Linear Regression for Northeast United States
Yang, J.; Astitha, M.; Schwartz, C. S.
2017-12-01
Bayesian linear regression (BLR) is a post-processing technique in which regression coefficients are derived and used to correct raw forecasts based on pairs of observation-model values. This study presents the development and application of a gridded Bayesian linear regression (GBLR) as a new post-processing technique to improve numerical weather prediction (NWP) of rain and wind storm forecasts over northeast United States. Ten controlled variables produced from ten ensemble members of the National Center for Atmospheric Research (NCAR) real-time prediction system are used for a GBLR model. In the GBLR framework, leave-one-storm-out cross-validation is utilized to study the performances of the post-processing technique in a database composed of 92 storms. To estimate the regression coefficients of the GBLR, optimization procedures that minimize the systematic and random error of predicted atmospheric variables (wind speed, precipitation, etc.) are implemented for the modeled-observed pairs of training storms. The regression coefficients calculated for meteorological stations of the National Weather Service are interpolated back to the model domain. An analysis of forecast improvements based on error reductions during the storms will demonstrate the value of GBLR approach. This presentation will also illustrate how the variances are optimized for the training partition in GBLR and discuss the verification strategy for grid points where no observations are available. The new post-processing technique is successful in improving wind speed and precipitation storm forecasts using past event-based data and has the potential to be implemented in real-time.
Durand, S.; Tellier, C. R.
1996-02-01
This paper constitutes the first part of a work devoted to applications of piezoresistance effects in germanium and silicon semiconductors. In this part, emphasis is placed on a formal explanation of non-linear effects. We propose a brief phenomenological description based on the multi-valleys model of semiconductors before to adopt a macroscopic tensorial model from which general analytical expressions for primed non-linear piezoresistance coefficients are derived. Graphical representations of linear and non-linear piezoresistance coefficients allows us to characterize the influence of the two angles of cut and of directions of alignment. The second part will primarily deal with specific applications for piezoresistive sensors. Cette publication constitue la première partie d'un travail consacré aux applications des effets piézorésistifs dans les semiconducteurs germanium et silicium. Cette partie traite essentiellement de la modélisation des effets non-linéaires. Après une description phénoménologique à partir du modèle de bande des semiconducteurs nous développons un modèle tensoriel macroscopique et nous proposons des équations générales analytiques exprimant les coefficients piézorésistifs non-linéaires dans des repères tournés. Des représentations graphiques des variations des coefficients piézorésistifs linéaires et non-linéaires permettent une pré-caractérisation de l'influence des angles de coupes et des directions d'alignement avant l'étude d'applications spécifiques qui feront l'objet de la deuxième partie.
Morales, Esteban; de Leon, John Mark S; Abdollahi, Niloufar; Yu, Fei; Nouri-Mahdavi, Kouros; Caprioli, Joseph
2016-03-01
The study was conducted to evaluate threshold smoothing algorithms to enhance prediction of the rates of visual field (VF) worsening in glaucoma. We studied 798 patients with primary open-angle glaucoma and 6 or more years of follow-up who underwent 8 or more VF examinations. Thresholds at each VF location for the first 4 years or first half of the follow-up time (whichever was greater) were smoothed with clusters defined by the nearest neighbor (NN), Garway-Heath, Glaucoma Hemifield Test (GHT), and weighting by the correlation of rates at all other VF locations. Thresholds were regressed with a pointwise exponential regression (PER) model and a pointwise linear regression (PLR) model. Smaller root mean square error (RMSE) values of the differences between the observed and the predicted thresholds at last two follow-ups indicated better model predictions. The mean (SD) follow-up times for the smoothing and prediction phase were 5.3 (1.5) and 10.5 (3.9) years. The mean RMSE values for the PER and PLR models were unsmoothed data, 6.09 and 6.55; NN, 3.40 and 3.42; Garway-Heath, 3.47 and 3.48; GHT, 3.57 and 3.74; and correlation of rates, 3.59 and 3.64. Smoothed VF data predicted better than unsmoothed data. Nearest neighbor provided the best predictions; PER also predicted consistently more accurately than PLR. Smoothing algorithms should be used when forecasting VF results with PER or PLR. The application of smoothing algorithms on VF data can improve forecasting in VF points to assist in treatment decisions.
Characteristics and Properties of a Simple Linear Regression Model
Kowal Robert
2016-12-01
Full Text Available A simple linear regression model is one of the pillars of classic econometrics. Despite the passage of time, it continues to raise interest both from the theoretical side as well as from the application side. One of the many fundamental questions in the model concerns determining derivative characteristics and studying the properties existing in their scope, referring to the first of these aspects. The literature of the subject provides several classic solutions in that regard. In the paper, a completely new design is proposed, based on the direct application of variance and its properties, resulting from the non-correlation of certain estimators with the mean, within the scope of which some fundamental dependencies of the model characteristics are obtained in a much more compact manner. The apparatus allows for a simple and uniform demonstration of multiple dependencies and fundamental properties in the model, and it does it in an intuitive manner. The results were obtained in a classic, traditional area, where everything, as it might seem, has already been thoroughly studied and discovered.
Exhaustive Search for Sparse Variable Selection in Linear Regression
Igarashi, Yasuhiko; Takenaka, Hikaru; Nakanishi-Ohno, Yoshinori; Uemura, Makoto; Ikeda, Shiro; Okada, Masato
2018-04-01
We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.
A Linear Regression Model for Global Solar Radiation on Horizontal Surfaces at Warri, Nigeria
Michael S. Okundamiya
2013-10-01
Full Text Available The growing anxiety on the negative effects of fossil fuels on the environment and the global emission reduction targets call for a more extensive use of renewable energy alternatives. Efficient solar energy utilization is an essential solution to the high atmospheric pollution caused by fossil fuel combustion. Global solar radiation (GSR data, which are useful for the design and evaluation of solar energy conversion system, are not measured at the forty-five meteorological stations in Nigeria. The dearth of the measured solar radiation data calls for accurate estimation. This study proposed a temperature-based linear regression, for predicting the monthly average daily GSR on horizontal surfaces, at Warri (latitude 5.020N and longitude 7.880E an oil city located in the south-south geopolitical zone, in Nigeria. The proposed model is analyzed based on five statistical indicators (coefficient of correlation, coefficient of determination, mean bias error, root mean square error, and t-statistic, and compared with the existing sunshine-based model for the same study. The results indicate that the proposed temperature-based linear regression model could replace the existing sunshine-based model for generating global solar radiation data. Keywords: air temperature; empirical model; global solar radiation; regression analysis; renewable energy; Warri
Research on the multiple linear regression in non-invasive blood glucose measurement.
Zhu, Jianming; Chen, Zhencheng
2015-01-01
A non-invasive blood glucose measurement sensor and the data process algorithm based on the metabolic energy conservation (MEC) method are presented in this paper. The physiological parameters of human fingertip can be measured by various sensing modalities, and blood glucose value can be evaluated with the physiological parameters by the multiple linear regression analysis. Five methods such as enter, remove, forward, backward and stepwise in multiple linear regression were compared, and the backward method had the best performance. The best correlation coefficient was 0.876 with the standard error of the estimate 0.534, and the significance was 0.012 (sig. regression equation was valid. The Clarke error grid analysis was performed to compare the MEC method with the hexokinase method, using 200 data points. The correlation coefficient R was 0.867 and all of the points were located in Zone A and Zone B, which shows the MEC method provides a feasible and valid way for non-invasive blood glucose measurement.
Partially linear varying coefficient models stratified by a functional covariate
Maity, Arnab; Huang, Jianhua Z.
2012-01-01
We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric
Weibull and lognormal Taguchi analysis using multiple linear regression
Piña-Monarrez, Manuel R.; Ortiz-Yañez, Jesús F.
2015-01-01
The paper provides to reliability practitioners with a method (1) to estimate the robust Weibull family when the Taguchi method (TM) is applied, (2) to estimate the normal operational Weibull family in an accelerated life testing (ALT) analysis to give confidence to the extrapolation and (3) to perform the ANOVA analysis to both the robust and the normal operational Weibull family. On the other hand, because the Weibull distribution neither has the normal additive property nor has a direct relationship with the normal parameters (µ, σ), in this paper, the issues of estimating a Weibull family by using a design of experiment (DOE) are first addressed by using an L_9 (3"4) orthogonal array (OA) in both the TM and in the Weibull proportional hazard model approach (WPHM). Then, by using the Weibull/Gumbel and the lognormal/normal relationships and multiple linear regression, the direct relationships between the Weibull and the lifetime parameters are derived and used to formulate the proposed method. Moreover, since the derived direct relationships always hold, the method is generalized to the lognormal and ALT analysis. Finally, the method’s efficiency is shown through its application to the used OA and to a set of ALT data. - Highlights: • It gives the statistical relations and steps to use the Taguchi Method (TM) to analyze Weibull data. • It gives the steps to determine the unknown Weibull family to both the robust TM setting and the normal ALT level. • It gives a method to determine the expected lifetimes and to perform its ANOVA analysis in TM and ALT analysis. • It gives a method to give confidence to the extrapolation in an ALT analysis by using the Weibull family of the normal level.
EPMLR: sequence-based linear B-cell epitope prediction method using multiple linear regression.
Lian, Yao; Ge, Meng; Pan, Xian-Ming
2014-12-19
B-cell epitopes have been studied extensively due to their immunological applications, such as peptide-based vaccine development, antibody production, and disease diagnosis and therapy. Despite several decades of research, the accurate prediction of linear B-cell epitopes has remained a challenging task. In this work, based on the antigen's primary sequence information, a novel linear B-cell epitope prediction model was developed using the multiple linear regression (MLR). A 10-fold cross-validation test on a large non-redundant dataset was performed to evaluate the performance of our model. To alleviate the problem caused by the noise of negative dataset, 300 experiments utilizing 300 sub-datasets were performed. We achieved overall sensitivity of 81.8%, precision of 64.1% and area under the receiver operating characteristic curve (AUC) of 0.728. We have presented a reliable method for the identification of linear B cell epitope using antigen's primary sequence information. Moreover, a web server EPMLR has been developed for linear B-cell epitope prediction: http://www.bioinfo.tsinghua.edu.cn/epitope/EPMLR/ .
Yunfeng Wu
2014-01-01
Full Text Available This paper presents a novel adaptive linear and normalized combination (ALNC method that can be used to combine the component radial basis function networks (RBFNs to implement better function approximation and regression tasks. The optimization of the fusion weights is obtained by solving a constrained quadratic programming problem. According to the instantaneous errors generated by the component RBFNs, the ALNC is able to perform the selective ensemble of multiple leaners by adaptively adjusting the fusion weights from one instance to another. The results of the experiments on eight synthetic function approximation and six benchmark regression data sets show that the ALNC method can effectively help the ensemble system achieve a higher accuracy (measured in terms of mean-squared error and the better fidelity (characterized by normalized correlation coefficient of approximation, in relation to the popular simple average, weighted average, and the Bagging methods.
Significance tests to determine the direction of effects in linear regression models.
Wiedermann, Wolfgang; Hagmann, Michael; von Eye, Alexander
2015-02-01
Previous studies have discussed asymmetric interpretations of the Pearson correlation coefficient and have shown that higher moments can be used to decide on the direction of dependence in the bivariate linear regression setting. The current study extends this approach by illustrating that the third moment of regression residuals may also be used to derive conclusions concerning the direction of effects. Assuming non-normally distributed variables, it is shown that the distribution of residuals of the correctly specified regression model (e.g., Y is regressed on X) is more symmetric than the distribution of residuals of the competing model (i.e., X is regressed on Y). Based on this result, 4 one-sample tests are discussed which can be used to decide which variable is more likely to be the response and which one is more likely to be the explanatory variable. A fifth significance test is proposed based on the differences of skewness estimates, which leads to a more direct test of a hypothesis that is compatible with direction of dependence. A Monte Carlo simulation study was performed to examine the behaviour of the procedures under various degrees of associations, sample sizes, and distributional properties of the underlying population. An empirical example is given which illustrates the application of the tests in practice. © 2014 The British Psychological Society.
Least Squares Adjustment: Linear and Nonlinear Weighted Regression Analysis
Nielsen, Allan Aasbjerg
2007-01-01
This note primarily describes the mathematics of least squares regression analysis as it is often used in geodesy including land surveying and satellite positioning applications. In these fields regression is often termed adjustment. The note also contains a couple of typical land surveying...... and satellite positioning application examples. In these application areas we are typically interested in the parameters in the model typically 2- or 3-D positions and not in predictive modelling which is often the main concern in other regression analysis applications. Adjustment is often used to obtain...... the clock error) and to obtain estimates of the uncertainty with which the position is determined. Regression analysis is used in many other fields of application both in the natural, the technical and the social sciences. Examples may be curve fitting, calibration, establishing relationships between...
Adachi, Daiki; Nishiguchi, Shu; Fukutani, Naoto; Hotta, Takayuki; Tashiro, Yuto; Morino, Saori; Shirooka, Hidehiko; Nozaki, Yuma; Hirata, Hinako; Yamaguchi, Moe; Yorozu, Ayanori; Takahashi, Masaki; Aoyama, Tomoki
2017-05-01
The purpose of this study was to investigate which spatial and temporal parameters of the Timed Up and Go (TUG) test are associated with motor function in elderly individuals. This study included 99 community-dwelling women aged 72.9 ± 6.3 years. Step length, step width, single support time, variability of the aforementioned parameters, gait velocity, cadence, reaction time from starting signal to first step, and minimum distance between the foot and a marker placed to 3 in front of the chair were measured using our analysis system. The 10-m walk test, five times sit-to-stand (FTSTS) test, and one-leg standing (OLS) test were used to assess motor function. Stepwise multivariate linear regression analysis was used to determine which TUG test parameters were associated with each motor function test. Finally, we calculated a predictive model for each motor function test using each regression coefficient. In stepwise linear regression analysis, step length and cadence were significantly associated with the 10-m walk test, FTSTS and OLS test. Reaction time was associated with the FTSTS test, and step width was associated with the OLS test. Each predictive model showed a strong correlation with the 10-m walk test and OLS test (P motor function test. Moreover, the TUG test time regarded as the lower extremity function and mobility has strong predictive ability in each motor function test. Copyright © 2017 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved.
Robust best linear estimation for regression analysis using surrogate and instrumental variables.
Wang, C Y
2012-04-01
We investigate methods for regression analysis when covariates are measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies the classical measurement error model, but it may not have repeated measurements. In addition to the surrogate variables that are available among the subjects in the calibration sample, we assume that there is an instrumental variable (IV) that is available for all study subjects. An IV is correlated with the unobserved true exposure variable and hence can be useful in the estimation of the regression coefficients. We propose a robust best linear estimator that uses all the available data, which is the most efficient among a class of consistent estimators. The proposed estimator is shown to be consistent and asymptotically normal under very weak distributional assumptions. For Poisson or linear regression, the proposed estimator is consistent even if the measurement error from the surrogate or IV is heteroscedastic. Finite-sample performance of the proposed estimator is examined and compared with other estimators via intensive simulation studies. The proposed method and other methods are applied to a bladder cancer case-control study.
Distributed Monitoring of the R(sup 2) Statistic for Linear Regression
Bhaduri, Kanishka; Das, Kamalika; Giannella, Chris R.
2011-01-01
The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and one or more dependent target variables. This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings. Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the updated model is broadcast back to all nodes. We show empirically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness.
An evaluation of bias in propensity score-adjusted non-linear regression models.
Wan, Fei; Mitra, Nandita
2018-03-01
Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.
Linear regression models for quantitative assessment of left ...
STORAGESEVER
2008-07-04
Jul 4, 2008 ... of left ventricular function and structures using M-mode echocardiography ... Pearson's correlation coefficients were computed. Tests were two tailed ... tation may be problematic in some subjects. Excellent temporal ... excluded were subjects with obstructive airway disease, sickle cell disease, pregnancy ...
SPSS and SAS programs for comparing Pearson correlations and OLS regression coefficients.
Weaver, Bruce; Wuensch, Karl L
2013-09-01
Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of these tests have not yet been implemented in popular statistical software packages such as SPSS and SAS. In this article, we describe all of the most common tests and provide SPSS and SAS programs to perform them. When they are applicable, our code also computes 100 × (1 - α)% confidence intervals corresponding to the tests. For testing hypotheses about independent regression coefficients, we demonstrate one method that uses summary data and another that uses raw data (i.e., Potthoff analysis). When the raw data are available, the latter method is preferred, because use of summary data entails some loss of precision due to rounding.
Multivariate linear regression of high-dimensional fMRI data with multiple target variables.
Valente, Giancarlo; Castellanos, Agustin Lage; Vanacore, Gianluca; Formisano, Elia
2014-05-01
Multivariate regression is increasingly used to study the relation between fMRI spatial activation patterns and experimental stimuli or behavioral ratings. With linear models, informative brain locations are identified by mapping the model coefficients. This is a central aspect in neuroimaging, as it provides the sought-after link between the activity of neuronal populations and subject's perception, cognition or behavior. Here, we show that mapping of informative brain locations using multivariate linear regression (MLR) may lead to incorrect conclusions and interpretations. MLR algorithms for high dimensional data are designed to deal with targets (stimuli or behavioral ratings, in fMRI) separately, and the predictive map of a model integrates information deriving from both neural activity patterns and experimental design. Not accounting explicitly for the presence of other targets whose associated activity spatially overlaps with the one of interest may lead to predictive maps of troublesome interpretation. We propose a new model that can correctly identify the spatial patterns associated with a target while achieving good generalization. For each target, the training is based on an augmented dataset, which includes all remaining targets. The estimation on such datasets produces both maps and interaction coefficients, which are then used to generalize. The proposed formulation is independent of the regression algorithm employed. We validate this model on simulated fMRI data and on a publicly available dataset. Results indicate that our method achieves high spatial sensitivity and good generalization and that it helps disentangle specific neural effects from interaction with predictive maps associated with other targets. Copyright © 2013 Wiley Periodicals, Inc.
Partially linear varying coefficient models stratified by a functional covariate
Maity, Arnab
2012-10-01
We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.
Linear regression models for quantitative assessment of left ...
Changes in left ventricular structures and function have been reported in cardiomyopathies. No prediction models have been established in this environment. This study established regression models for prediction of left ventricular structures in normal subjects. A sample of normal subjects was drawn from a large urban ...
Linearity and Misspecification Tests for Vector Smooth Transition Regression Models
Teräsvirta, Timo; Yang, Yukai
The purpose of the paper is to derive Lagrange multiplier and Lagrange multiplier type specification and misspecification tests for vector smooth transition regression models. We report results from simulation studies in which the size and power properties of the proposed asymptotic tests in small...
Using multiple linear regression techniques to quantify carbon ...
Fallow ecosystems provide a significant carbon stock that can be quantified for inclusion in the accounts of global carbon budgets. Process and statistical models of productivity, though useful, are often technically rigid as the conditions for their application are not easy to satisfy. Multiple regression techniques have been ...
Interpreting Multiple Linear Regression: A Guidebook of Variable Importance
Nathans, Laura L.; Oswald, Frederick L.; Nimon, Kim
2012-01-01
Multiple regression (MR) analyses are commonly employed in social science fields. It is also common for interpretation of results to typically reflect overreliance on beta weights, often resulting in very limited interpretations of variable importance. It appears that few researchers employ other methods to obtain a fuller understanding of what…
Testing for marginal linear effects in quantile regression
Wang, Huixia Judy
2017-10-23
The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the test proposed is applicable and computationally feasible for large dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response. The approach is illustrated by using an application to a human immunodeficiency virus drug resistance data set.
Testing for marginal linear effects in quantile regression
Wang, Huixia Judy; McKeague, Ian W.; Qian, Min
2017-01-01
The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the test proposed is applicable and computationally feasible for large dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response. The approach is illustrated by using an application to a human immunodeficiency virus drug resistance data set.
Dlugosz, Stephan; Mammen, Enno; Wilke, Ralf
We consider the semiparametric generalised linear regression model which has mainstream empirical models such as the (partially) linear mean regression, logistic and multinomial regression as special cases. As an extension to related literature we allow a misclassified covariate to be interacted...
Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment
Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos
2013-01-01
In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…
Variable selection in multiple linear regression: The influence of ...
provide an indication of whether the fit of the selected model improves or ... and calculate M(−i); quantify the influence of case i in terms of a function, f(•), of M and ..... [21] Venter JH & Snyman JLJ, 1997, Linear model selection based on risk ...
An introduction to using Bayesian linear regression with clinical data.
Baldwin, Scott A; Larson, Michael J
2017-11-01
Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.
Electricity consumption forecasting in Italy using linear regression models
Bianco, Vincenzo; Manca, Oronzio; Nardini, Sergio [DIAM, Seconda Universita degli Studi di Napoli, Via Roma 29, 81031 Aversa (CE) (Italy)
2009-09-15
The influence of economic and demographic variables on the annual electricity consumption in Italy has been investigated with the intention to develop a long-term consumption forecasting model. The time period considered for the historical data is from 1970 to 2007. Different regression models were developed, using historical electricity consumption, gross domestic product (GDP), gross domestic product per capita (GDP per capita) and population. A first part of the paper considers the estimation of GDP, price and GDP per capita elasticities of domestic and non-domestic electricity consumption. The domestic and non-domestic short run price elasticities are found to be both approximately equal to -0.06, while long run elasticities are equal to -0.24 and -0.09, respectively. On the contrary, the elasticities of GDP and GDP per capita present higher values. In the second part of the paper, different regression models, based on co-integrated or stationary data, are presented. Different statistical tests are employed to check the validity of the proposed models. A comparison with national forecasts, based on complex econometric models, such as Markal-Time, was performed, showing that the developed regressions are congruent with the official projections, with deviations of {+-}1% for the best case and {+-}11% for the worst. These deviations are to be considered acceptable in relation to the time span taken into account. (author)
Electricity consumption forecasting in Italy using linear regression models
Bianco, Vincenzo; Manca, Oronzio; Nardini, Sergio
2009-01-01
The influence of economic and demographic variables on the annual electricity consumption in Italy has been investigated with the intention to develop a long-term consumption forecasting model. The time period considered for the historical data is from 1970 to 2007. Different regression models were developed, using historical electricity consumption, gross domestic product (GDP), gross domestic product per capita (GDP per capita) and population. A first part of the paper considers the estimation of GDP, price and GDP per capita elasticities of domestic and non-domestic electricity consumption. The domestic and non-domestic short run price elasticities are found to be both approximately equal to -0.06, while long run elasticities are equal to -0.24 and -0.09, respectively. On the contrary, the elasticities of GDP and GDP per capita present higher values. In the second part of the paper, different regression models, based on co-integrated or stationary data, are presented. Different statistical tests are employed to check the validity of the proposed models. A comparison with national forecasts, based on complex econometric models, such as Markal-Time, was performed, showing that the developed regressions are congruent with the official projections, with deviations of ±1% for the best case and ±11% for the worst. These deviations are to be considered acceptable in relation to the time span taken into account. (author)
Relative Importance for Linear Regression in R: The Package relaimpo
Groemping, Ulrike
2006-01-01
Relative importance is a topic that has seen a lot of interest in recent years, particularly in applied work. The R package relaimpo implements six different metrics for assessing relative importance of regressors in the linear model, two of which are recommended - averaging over orderings of regressors and a newly proposed metric (Feldman 2005) called pmvd. Apart from delivering the metrics themselves, relaimpo also provides (exploratory) bootstrap confidence intervals. This paper offers a b...
Corsetti, James A; Green, William E; Ellis, Jonathan D; Schmidt, Greg R; Moore, Duncan T
2016-10-10
Characterizing the thermal properties of optical materials is necessary for understanding how to design an optical system for changing environmental conditions. A method is presented for simultaneously measuring both the linear coefficient of thermal expansion and the temperature-dependent refractive index coefficient of a sample interferometrically in air. Both the design and fabrication of the interferometer is presented as well as a discussion of the results of measuring both a steel and a CaF2 sample.
Yubo Wang
2017-06-01
Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Wang, Yubo; Veluvolu, Kalyana C
2017-06-14
It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Linear Regression between CIE-Lab Color Parameters and Organic Matter in Soils of Tea Plantations
Chen, Yonggen; Zhang, Min; Fan, Dongmei; Fan, Kai; Wang, Xiaochang
2018-02-01
To quantify the relationship between the soil organic matter and color parameters using the CIE-Lab system, 62 soil samples (0-10 cm, Ferralic Acrisols) from tea plantations were collected from southern China. After air-drying and sieving, numerical color information and reflectance spectra of soil samples were measured under laboratory conditions using an UltraScan VIS (HunterLab) spectrophotometer equipped with CIE-Lab color models. We found that soil total organic carbon (TOC) and nitrogen (TN) contents were negatively correlated with the L* value (lightness) ( r = -0.84 and -0.80, respectively), a* value (correlation coefficient r = -0.51 and -0.46, respectively) and b* value ( r = -0.76 and -0.70, respectively). There were also linear regressions between TOC and TN contents with the L* value and b* value. Results showed that color parameters from a spectrophotometer equipped with CIE-Lab color models can predict TOC contents well for soils in tea plantations. The linear regression model between color values and soil organic carbon contents showed it can be used as a rapid, cost-effective method to evaluate content of soil organic matter in Chinese tea plantations.
Hecht, Jeffrey B.
The analysis of regression residuals and detection of outliers are discussed, with emphasis on determining how deviant an individual data point must be to be considered an outlier and the impact that multiple suspected outlier data points have on the process of outlier determination and treatment. Only bivariate (one dependent and one independent)…
Two biased estimation techniques in linear regression: Application to aircraft
Klein, Vladislav
1988-01-01
Several ways for detection and assessment of collinearity in measured data are discussed. Because data collinearity usually results in poor least squares estimates, two estimation techniques which can limit a damaging effect of collinearity are presented. These two techniques, the principal components regression and mixed estimation, belong to a class of biased estimation techniques. Detection and assessment of data collinearity and the two biased estimation techniques are demonstrated in two examples using flight test data from longitudinal maneuvers of an experimental aircraft. The eigensystem analysis and parameter variance decomposition appeared to be a promising tool for collinearity evaluation. The biased estimators had far better accuracy than the results from the ordinary least squares technique.
Xia, Yin; Cai, Tianxi; Cai, T Tony
2018-01-01
Motivated by applications in genomics, we consider in this paper global and multiple testing for the comparisons of two high-dimensional linear regression models. A procedure for testing the equality of the two regression vectors globally is proposed and shown to be particularly powerful against sparse alternatives. We then introduce a multiple testing procedure for identifying unequal coordinates while controlling the false discovery rate and false discovery proportion. Theoretical justifications are provided to guarantee the validity of the proposed tests and optimality results are established under sparsity assumptions on the regression coefficients. The proposed testing procedures are easy to implement. Numerical properties of the procedures are investigated through simulation and data analysis. The results show that the proposed tests maintain the desired error rates under the null and have good power under the alternative at moderate sample sizes. The procedures are applied to the Framingham Offspring study to investigate the interactions between smoking and cardiovascular related genetic mutations important for an inflammation marker.
Soil moisture estimation using multi linear regression with terraSAR-X data
G. García
2016-06-01
Full Text Available The first five centimeters of soil form an interface where the main heat fluxes exchanges between the land surface and the atmosphere occur. Besides ground measurements, remote sensing has proven to be an excellent tool for the monitoring of spatial and temporal distributed data of the most relevant Earth surface parameters including soil’s parameters. Indeed, active microwave sensors (Synthetic Aperture Radar - SAR offer the opportunity to monitor soil moisture (HS at global, regional and local scales by monitoring involved processes. Several inversion algorithms, that derive geophysical information as HS from SAR data, were developed. Many of them use electromagnetic models for simulating the backscattering coefficient and are based on statistical techniques, such as neural networks, inversion methods and regression models. Recent studies have shown that simple multiple regression techniques yield satisfactory results. The involved geophysical variables in these methodologies are descriptive of the soil structure, microwave characteristics and land use. Therefore, in this paper we aim at developing a multiple linear regression model to estimate HS on flat agricultural regions using TerraSAR-X satellite data and data from a ground weather station. The results show that the backscatter, the precipitation and the relative humidity are the explanatory variables of HS. The results obtained presented a RMSE of 5.4 and a R2 of about 0.6
Detection of epistatic effects with logic regression and a classical linear regression model.
Malina, Magdalena; Ickstadt, Katja; Schwender, Holger; Posch, Martin; Bogdan, Małgorzata
2014-02-01
To locate multiple interacting quantitative trait loci (QTL) influencing a trait of interest within experimental populations, usually methods as the Cockerham's model are applied. Within this framework, interactions are understood as the part of the joined effect of several genes which cannot be explained as the sum of their additive effects. However, if a change in the phenotype (as disease) is caused by Boolean combinations of genotypes of several QTLs, this Cockerham's approach is often not capable to identify them properly. To detect such interactions more efficiently, we propose a logic regression framework. Even though with the logic regression approach a larger number of models has to be considered (requiring more stringent multiple testing correction) the efficient representation of higher order logic interactions in logic regression models leads to a significant increase of power to detect such interactions as compared to a Cockerham's approach. The increase in power is demonstrated analytically for a simple two-way interaction model and illustrated in more complex settings with simulation study and real data analysis.
A simplified procedure of linear regression in a preliminary analysis
Silvia Facchinetti
2013-05-01
Full Text Available The analysis of a statistical large data-set can be led by the study of a particularly interesting variable Y – regressed – and an explicative variable X, chosen among the remained variables, conjointly observed. The study gives a simplified procedure to obtain the functional link of the variables y=y(x by a partition of the data-set into m subsets, in which the observations are synthesized by location indices (mean or median of X and Y. Polynomial models for y(x of order r are considered to verify the characteristics of the given procedure, in particular we assume r= 1 and 2. The distributions of the parameter estimators are obtained by simulation, when the fitting is done for m= r + 1. Comparisons of the results, in terms of distribution and efficiency, are made with the results obtained by the ordinary least square methods. The study also gives some considerations on the consistency of the estimated parameters obtained by the given procedure.
Uca; Toriman, Ekhwan; Jaafar, Othman; Maru, Rosmini; Arfan, Amal; Saleh Ahmar, Ansari
2018-01-01
Prediction of suspended sediment discharge in a catchments area is very important because it can be used to evaluation the erosion hazard, management of its water resources, water quality, hydrology project management (dams, reservoirs, and irrigation) and to determine the extent of the damage that occurred in the catchments. Multiple Linear Regression analysis and artificial neural network can be used to predict the amount of daily suspended sediment discharge. Regression analysis using the least square method, whereas artificial neural networks using Radial Basis Function (RBF) and feedforward multilayer perceptron with three learning algorithms namely Levenberg-Marquardt (LM), Scaled Conjugate Descent (SCD) and Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFGS). The number neuron of hidden layer is three to sixteen, while in output layer only one neuron because only one output target. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2 ) and coefficient of efficiency (CE) of the multiple linear regression (MLRg) value Model 2 (6 input variable independent) has the lowest the value of MAE and RMSE (0.0000002 and 13.6039) and highest R2 and CE (0.9971 and 0.9971). When compared between LM, SCG and RBF, the BFGS model structure 3-7-1 is the better and more accurate to prediction suspended sediment discharge in Jenderam catchment. The performance value in testing process, MAE and RMSE (13.5769 and 17.9011) is smallest, meanwhile R2 and CE (0.9999 and 0.9998) is the highest if it compared with the another BFGS Quasi-Newton model (6-3-1, 9-10-1 and 12-12-1). Based on the performance statistics value, MLRg, LM, SCG, BFGS and RBF suitable and accurately for prediction by modeling the non-linear complex behavior of suspended sediment responses to rainfall, water depth and discharge. The comparison between artificial neural network (ANN) and MLRg, the MLRg Model 2 accurately for to prediction suspended sediment discharge (kg
Deev, V.I.; Sobolev, V.P.; Kruglov, A.B.; Pridantsev, A.I.
1984-01-01
Results of experimental investigation of heat conduction coefficient and coefficient of linear thermal expansion and thermal shrinkages of the STEF-1 textolite-glass widely used in superconducting magnetic systems as electric insulating and structural material are presented. Samples of two types have been died: sample axisa is perpendicular to a plae of fiberglass layers ad sample axis is parallel to a plane of fiberglass layers. Heat conduction coefficient was decreased almost a five times with temperature decrease from 300 up to 5K and was slightly dependent on a sample type. Temperature variation of linear dimensions in a sample of the first type occurs in twice as fast as compared to the sample of the second type
Yolci Omeroglu, Perihan; Ambrus, Árpad; Boyacioglu, Dilek
2018-03-28
Determination of pesticide residues is based on calibration curves constructed for each batch of analysis. Calibration standard solutions are prepared from a known amount of reference material at different concentration levels covering the concentration range of the analyte in the analysed samples. In the scope of this study, the applicability of both ordinary linear and weighted linear regression (OLR and WLR) for pesticide residue analysis was investigated. We used 782 multipoint calibration curves obtained for 72 different analytical batches with high-pressure liquid chromatography equipped with an ultraviolet detector, and gas chromatography with electron capture, nitrogen phosphorus or mass spectrophotometer detectors. Quality criteria of the linear curves including regression coefficient, standard deviation of relative residuals and deviation of back calculated concentrations were calculated both for WLR and OLR methods. Moreover, the relative uncertainty of the predicted analyte concentration was estimated for both methods. It was concluded that calibration curve based on WLR complies with all the quality criteria set by international guidelines compared to those calculated with OLR. It means that all the data fit well with WLR for pesticide residue analysis. It was estimated that, regardless of the actual concentration range of the calibration, relative uncertainty at the lowest calibrated level ranged between 0.3% and 113.7% for OLR and between 0.2% and 22.1% for WLR. At or above 1/3 of the calibrated range, uncertainty of calibration curve ranged between 0.1% and 16.3% for OLR and 0% and 12.2% for WLR, and therefore, the two methods gave comparable results.
The performance of random coefficient regression in accounting for residual confounding.
Gustafson, Paul; Greenland, Sander
2006-09-01
Greenland (2000, Biometrics 56, 915-921) describes the use of random coefficient regression to adjust for residual confounding in a particular setting. We examine this setting further, giving theoretical and empirical results concerning the frequentist and Bayesian performance of random coefficient regression. Particularly, we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding. This devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model. The approach described by Gustafson (2005, Statistical Science 20, 111-140) is used to quantify the performance of a Bayesian estimator arising from a nonidentified model. From both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints. In terms of point-estimator bias this superiority arises when the extent of residual confounding is substantial, but the advantage is much broader in terms of interval estimation. The benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality, for the standard identifying constraints are equivalent to priors that typically correspond much worse.
Identifying predictors of physics item difficulty: A linear regression approach
Mesic, Vanes; Muratovic, Hasnija
2011-06-01
Large-scale assessments of student achievement in physics are often approached with an intention to discriminate students based on the attained level of their physics competencies. Therefore, for purposes of test design, it is important that items display an acceptable discriminatory behavior. To that end, it is recommended to avoid extraordinary difficult and very easy items. Knowing the factors that influence physics item difficulty makes it possible to model the item difficulty even before the first pilot study is conducted. Thus, by identifying predictors of physics item difficulty, we can improve the test-design process. Furthermore, we get additional qualitative feedback regarding the basic aspects of student cognitive achievement in physics that are directly responsible for the obtained, quantitative test results. In this study, we conducted a secondary analysis of data that came from two large-scale assessments of student physics achievement at the end of compulsory education in Bosnia and Herzegovina. Foremost, we explored the concept of “physics competence” and performed a content analysis of 123 physics items that were included within the above-mentioned assessments. Thereafter, an item database was created. Items were described by variables which reflect some basic cognitive aspects of physics competence. For each of the assessments, Rasch item difficulties were calculated in separate analyses. In order to make the item difficulties from different assessments comparable, a virtual test equating procedure had to be implemented. Finally, a regression model of physics item difficulty was created. It has been shown that 61.2% of item difficulty variance can be explained by factors which reflect the automaticity, complexity, and modality of the knowledge structure that is relevant for generating the most probable correct solution, as well as by the divergence of required thinking and interference effects between intuitive and formal physics knowledge
Identifying predictors of physics item difficulty: A linear regression approach
Hasnija Muratovic
2011-06-01
Full Text Available Large-scale assessments of student achievement in physics are often approached with an intention to discriminate students based on the attained level of their physics competencies. Therefore, for purposes of test design, it is important that items display an acceptable discriminatory behavior. To that end, it is recommended to avoid extraordinary difficult and very easy items. Knowing the factors that influence physics item difficulty makes it possible to model the item difficulty even before the first pilot study is conducted. Thus, by identifying predictors of physics item difficulty, we can improve the test-design process. Furthermore, we get additional qualitative feedback regarding the basic aspects of student cognitive achievement in physics that are directly responsible for the obtained, quantitative test results. In this study, we conducted a secondary analysis of data that came from two large-scale assessments of student physics achievement at the end of compulsory education in Bosnia and Herzegovina. Foremost, we explored the concept of “physics competence” and performed a content analysis of 123 physics items that were included within the above-mentioned assessments. Thereafter, an item database was created. Items were described by variables which reflect some basic cognitive aspects of physics competence. For each of the assessments, Rasch item difficulties were calculated in separate analyses. In order to make the item difficulties from different assessments comparable, a virtual test equating procedure had to be implemented. Finally, a regression model of physics item difficulty was created. It has been shown that 61.2% of item difficulty variance can be explained by factors which reflect the automaticity, complexity, and modality of the knowledge structure that is relevant for generating the most probable correct solution, as well as by the divergence of required thinking and interference effects between intuitive and formal
Transport coefficients from SU(3) Polyakov linear-σ model
Tawfik, A.; Diab, A.
2015-01-01
In the mean field approximation, the grand potential of SU(3) Polyakov linear-σ model (PLSM) is analyzed for the order parameter of the light and strange chiral phase-transitions, σ l and σ s , respectively, and for the deconfinement order parameters φ and φ*. Furthermore, the subtracted condensate Δ l,s and the chiral order-parameters M b are compared with lattice QCD calculations. By using the dynamical quasiparticle model (DQPM), which can be considered as a system of noninteracting massive quasiparticles, we have evaluated the decay width and the relaxation time of quarks and gluons. In the framework of LSM and with Polyakov loop corrections included, the interaction measure Δ/T 4 , the specific heat c v and speed of sound squared c s 2 have been determined, as well as the temperature dependence of the normalized quark number density n q /T 3 and the quark number susceptibilities χ q /T 2 at various values of the baryon chemical potential. The electric and heat conductivity, σ e and κ, and the bulk and shear viscosities normalized to the thermal entropy, ζ/s and η/s, are compared with available results of lattice QCD calculations.
Liu, Pudong; Shi, Runhe; Wang, Hong; Bai, Kaixu; Gao, Wei
2014-10-01
Leaf pigments are key elements for plant photosynthesis and growth. Traditional manual sampling of these pigments is labor-intensive and costly, which also has the difficulty in capturing their temporal and spatial characteristics. The aim of this work is to estimate photosynthetic pigments at large scale by remote sensing. For this purpose, inverse model were proposed with the aid of stepwise multiple linear regression (SMLR) analysis. Furthermore, a leaf radiative transfer model (i.e. PROSPECT model) was employed to simulate the leaf reflectance where wavelength varies from 400 to 780 nm at 1 nm interval, and then these values were treated as the data from remote sensing observations. Meanwhile, simulated chlorophyll concentration (Cab), carotenoid concentration (Car) and their ratio (Cab/Car) were taken as target to build the regression model respectively. In this study, a total of 4000 samples were simulated via PROSPECT with different Cab, Car and leaf mesophyll structures as 70% of these samples were applied for training while the last 30% for model validation. Reflectance (r) and its mathematic transformations (1/r and log (1/r)) were all employed to build regression model respectively. Results showed fair agreements between pigments and simulated reflectance with all adjusted coefficients of determination (R2) larger than 0.8 as 6 wavebands were selected to build the SMLR model. The largest value of R2 for Cab, Car and Cab/Car are 0.8845, 0.876 and 0.8765, respectively. Meanwhile, mathematic transformations of reflectance showed little influence on regression accuracy. We concluded that it was feasible to estimate the chlorophyll and carotenoids and their ratio based on statistical model with leaf reflectance data.
Jakubowski, J.; Stypulkowski, J. B.; Bernardeau, F. G.
2017-12-01
The first phase of the Abu Hamour drainage and storm tunnel was completed in early 2017. The 9.5 km long, 3.7 m diameter tunnel was excavated with two Earth Pressure Balance (EPB) Tunnel Boring Machines from Herrenknecht. TBM operation processes were monitored and recorded by Data Acquisition and Evaluation System. The authors coupled collected TBM drive data with available information on rock mass properties, cleansed, completed with secondary variables and aggregated by weeks and shifts. Correlations and descriptive statistics charts were examined. Multivariate Linear Regression and CART regression tree models linking TBM penetration rate (PR), penetration per revolution (PPR) and field penetration index (FPI) with TBM operational and geotechnical characteristics were performed for the conditions of the weak/soft rock of Doha. Both regression methods are interpretable and the data were screened with different computational approaches allowing enriched insight. The primary goal of the analysis was to investigate empirical relations between multiple explanatory and responding variables, to search for best subsets of explanatory variables and to evaluate the strength of linear and non-linear relations. For each of the penetration indices, a predictive model coupling both regression methods was built and validated. The resultant models appeared to be stronger than constituent ones and indicated an opportunity for more accurate and robust TBM performance predictions.
Freitas, Alex A; Limbu, Kriti; Ghafourian, Taravat
2015-01-01
Volume of distribution is an important pharmacokinetic property that indicates the extent of a drug's distribution in the body tissues. This paper addresses the problem of how to estimate the apparent volume of distribution at steady state (Vss) of chemical compounds in the human body using decision tree-based regression methods from the area of data mining (or machine learning). Hence, the pros and cons of several different types of decision tree-based regression methods have been discussed. The regression methods predict Vss using, as predictive features, both the compounds' molecular descriptors and the compounds' tissue:plasma partition coefficients (Kt:p) - often used in physiologically-based pharmacokinetics. Therefore, this work has assessed whether the data mining-based prediction of Vss can be made more accurate by using as input not only the compounds' molecular descriptors but also (a subset of) their predicted Kt:p values. Comparison of the models that used only molecular descriptors, in particular, the Bagging decision tree (mean fold error of 2.33), with those employing predicted Kt:p values in addition to the molecular descriptors, such as the Bagging decision tree using adipose Kt:p (mean fold error of 2.29), indicated that the use of predicted Kt:p values as descriptors may be beneficial for accurate prediction of Vss using decision trees if prior feature selection is applied. Decision tree based models presented in this work have an accuracy that is reasonable and similar to the accuracy of reported Vss inter-species extrapolations in the literature. The estimation of Vss for new compounds in drug discovery will benefit from methods that are able to integrate large and varied sources of data and flexible non-linear data mining methods such as decision trees, which can produce interpretable models. Graphical AbstractDecision trees for the prediction of tissue partition coefficient and volume of distribution of drugs.
Describing Growth Pattern of Bali Cows Using Non-linear Regression Models
Mohd. Hafiz A.W
2016-12-01
Full Text Available The objective of this study was to evaluate the best fit non-linear regression model to describe the growth pattern of Bali cows. Estimates of asymptotic mature weight, rate of maturing and constant of integration were derived from Brody, von Bertalanffy, Gompertz and Logistic models which were fitted to cross-sectional data of body weight taken from 74 Bali cows raised in MARDI Research Station Muadzam Shah Pahang. Coefficient of determination (R2 and residual mean squares (MSE were used to determine the best fit model in describing the growth pattern of Bali cows. Von Bertalanffy model was the best model among the four growth functions evaluated to determine the mature weight of Bali cattle as shown by the highest R2 and lowest MSE values (0.973 and 601.9, respectively, followed by Gompertz (0.972 and 621.2, respectively, Logistic (0.971 and 648.4, respectively and Brody (0.932 and 660.5, respectively models. The correlation between rate of maturing and mature weight was found to be negative in the range of -0.170 to -0.929 for all models, indicating that animals of heavier mature weight had lower rate of maturing. The use of non-linear model could summarize the weight-age relationship into several biologically interpreted parameters compared to the entire lifespan weight-age data points that are difficult and time consuming to interpret.
MANCOVA for one way classification with homogeneity of regression coefficient vectors
Mokesh Rayalu, G.; Ravisankar, J.; Mythili, G. Y.
2017-11-01
The MANOVA and MANCOVA are the extensions of the univariate ANOVA and ANCOVA techniques to multidimensional or vector valued observations. The assumption of a Gaussian distribution has been replaced with the Multivariate Gaussian distribution for the vectors data and residual term variables in the statistical models of these techniques. The objective of MANCOVA is to determine if there are statistically reliable mean differences that can be demonstrated between groups later modifying the newly created variable. When randomization assignment of samples or subjects to groups is not possible, multivariate analysis of covariance (MANCOVA) provides statistical matching of groups by adjusting dependent variables as if all subjects scored the same on the covariates. In this research article, an extension has been made to the MANCOVA technique with more number of covariates and homogeneity of regression coefficient vectors is also tested.
Predicting Fuel Ignition Quality Using 1H NMR Spectroscopy and Multiple Linear Regression
Abdul Jameel, Abdul Gani
2016-09-14
An improved model for the prediction of ignition quality of hydrocarbon fuels has been developed using 1H nuclear magnetic resonance (NMR) spectroscopy and multiple linear regression (MLR) modeling. Cetane number (CN) and derived cetane number (DCN) of 71 pure hydrocarbons and 54 hydrocarbon blends were utilized as a data set to study the relationship between ignition quality and molecular structure. CN and DCN are functional equivalents and collectively referred to as D/CN, herein. The effect of molecular weight and weight percent of structural parameters such as paraffinic CH3 groups, paraffinic CH2 groups, paraffinic CH groups, olefinic CH–CH2 groups, naphthenic CH–CH2 groups, and aromatic C–CH groups on D/CN was studied. A particular emphasis on the effect of branching (i.e., methyl substitution) on the D/CN was studied, and a new parameter denoted as the branching index (BI) was introduced to quantify this effect. A new formula was developed to calculate the BI of hydrocarbon fuels using 1H NMR spectroscopy. Multiple linear regression (MLR) modeling was used to develop an empirical relationship between D/CN and the eight structural parameters. This was then used to predict the DCN of many hydrocarbon fuels. The developed model has a high correlation coefficient (R2 = 0.97) and was validated with experimentally measured DCN of twenty-two real fuel mixtures (e.g., gasolines and diesels) and fifty-nine blends of known composition, and the predicted values matched well with the experimental data.
Kim, T. W.; Park, G. H.
2014-12-01
Seasonal variation of aragonite saturation state (Ωarag) in the North Pacific Ocean (NPO) was investigated, using multiple linear regression (MLR) models produced from the PACIFICA (Pacific Ocean interior carbon) dataset. Data within depth ranges of 50-1200m were used to derive MLR models, and three parameters (potential temperature, nitrate, and apparent oxygen utilization (AOU)) were chosen as predictor variables because these parameters are associated with vertical mixing, DIC (dissolved inorganic carbon) removal and release which all affect Ωarag in water column directly or indirectly. The PACIFICA dataset was divided into 5° × 5° grids, and a MLR model was produced in each grid, giving total 145 independent MLR models over the NPO. Mean RMSE (root mean square error) and r2 (coefficient of determination) of all derived MLR models were approximately 0.09 and 0.96, respectively. Then the obtained MLR coefficients for each of predictor variables and an intercept were interpolated over the study area, thereby making possible to allocate MLR coefficients to data-sparse ocean regions. Predictability from the interpolated coefficients was evaluated using Hawaiian time-series data, and as a result mean residual between measured and predicted Ωarag values was approximately 0.08, which is less than the mean RMSE of our MLR models. The interpolated MLR coefficients were combined with seasonal climatology of World Ocean Atlas 2013 (1° × 1°) to produce seasonal Ωarag distributions over various depths. Large seasonal variability in Ωarag was manifested in the mid-latitude Western NPO (24-40°N, 130-180°E) and low-latitude Eastern NPO (0-12°N, 115-150°W). In the Western NPO, seasonal fluctuations of water column stratification appeared to be responsible for the seasonal variation in Ωarag (~ 0.5 at 50 m) because it closely followed temperature variations in a layer of 0-75 m. In contrast, remineralization of organic matter was the main cause for the seasonal
Kumar, K. Vasanth; Porkodi, K.; Rocha, F.
2008-01-01
A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r 2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r 2 ), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r 2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K 2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm
Boyarskij, S.V.
1986-01-01
Experimental results are presented for internal friction and linear expansion coefficient at zirconium and cobalt in the temperature range from 440 K to the point of the phase transition of the first kind (1138 K for Zr and 706 for Co). Anomalous changes of the internal friction and linear expansion coefficient in the phase transition region are found. Theoretical considerations are given to explain the sharp decrease of the internal friction as temperature approaches the phase transition point
Fuzzy solution of the linear programming problem with interval coefficients in the constraints
Dorota Kuchta
2005-01-01
A fuzzy concept of solving the linear programming problem with interval coefficients is proposed. For each optimism level of the decision maker (where the optimism concerns the certainty that no errors have been committed in the estimation of the interval coefficients and the belief that optimistic realisations of the interval coefficients will occur) another interval solution of the problem will be generated and the decision maker will be able to choose the final solution having a complete v...
An Analytical-empirical Calculation of Linear Attenuation Coefficient of Megavoltage Photon Beams.
Seif, F; Tahmasebi-Birgani, M J; Bayatiani, M R
2017-09-01
In this study, a method for linear attenuation coefficient calculation was introduced. Linear attenuation coefficient was calculated with a new method that base on the physics of interaction of photon with matter, mathematical calculation and x-ray spectrum consideration. The calculation was done for Cerrobend as a common radiotherapy modifier and Mercury. The values of calculated linear attenuation coefficient with this new method are in acceptable range. Also, the linear attenuation coefficient decreases slightly as the thickness of attenuating filter (Cerrobend or mercury) increased, so the procedure of linear attenuation coefficient variation is in agreement with other documents. The results showed that the attenuation ability of mercury was about 1.44 times more than Cerrobend. The method that was introduced in this study for linear attenuation coefficient calculation is general enough to treat beam modifiers with any shape or material by using the same formalism; however, calculating was made only for mercury and Cerrobend attenuator. On the other hand, it seems that this method is suitable for high energy shields or protector designing.
Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne
2012-12-01
In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.
As a fast and effective technique, the multiple linear regression (MLR) method has been widely used in modeling and prediction of beach bacteria concentrations. Among previous works on this subject, however, several issues were insufficiently or inconsistently addressed. Those is...
Predicting Fuel Ignition Quality Using 1H NMR Spectroscopy and Multiple Linear Regression
Abdul Jameel, Abdul Gani; Naser, Nimal; Emwas, Abdul-Hamid M.; Dooley, Stephen; Sarathy, Mani
2016-01-01
An improved model for the prediction of ignition quality of hydrocarbon fuels has been developed using 1H nuclear magnetic resonance (NMR) spectroscopy and multiple linear regression (MLR) modeling. Cetane number (CN) and derived cetane number (DCN
Tripepi, Giovanni; Jager, Kitty J.; Stel, Vianda S.; Dekker, Friedo W.; Zoccali, Carmine
2011-01-01
Because of some limitations of stratification methods, epidemiologists frequently use multiple linear and logistic regression analyses to address specific epidemiological questions. If the dependent variable is a continuous one (for example, systolic pressure and serum creatinine), the researcher
Volkov, A.G.; Kortov, S.V.; Povzner, A.A.
1996-01-01
The low temperature measurements of thermal coefficient of linear expansion of strong paramagnet FeSi are carried out. The results obtained are discussed with in the framework of spin-fluctuation theory. It is shown that electronic part of the thermal coefficient of linear expansion is negative in the range of temperatures lower that of the semiconductor-metal phase transition. In metal phase it becomes positive. This specific features of the thermal coefficient is explained by the spin-fluctuation renormalization of d-electronic states density
Analysis of γ spectra in airborne radioactivity measurements using multiple linear regressions
Bao Min; Shi Quanlin; Zhang Jiamei
2004-01-01
This paper describes the net peak counts calculating of nuclide 137 Cs at 662 keV of γ spectra in airborne radioactivity measurements using multiple linear regressions. Mathematic model is founded by analyzing every factor that has contribution to Cs peak counts in spectra, and multiple linear regression function is established. Calculating process adopts stepwise regression, and the indistinctive factors are eliminated by F check. The regression results and its uncertainty are calculated using Least Square Estimation, then the Cs peak net counts and its uncertainty can be gotten. The analysis results for experimental spectrum are displayed. The influence of energy shift and energy resolution on the analyzing result is discussed. In comparison with the stripping spectra method, multiple linear regression method needn't stripping radios, and the calculating result has relation with the counts in Cs peak only, and the calculating uncertainty is reduced. (authors)
Camporesi, Roberto
2011-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…
Enders, Felicity
2013-12-01
Although regression is widely used for reading and publishing in the medical literature, no instruments were previously available to assess students' understanding. The goal of this study was to design and assess such an instrument for graduate students in Clinical and Translational Science and Public Health. A 27-item REsearch on Global Regression Expectations in StatisticS (REGRESS) quiz was developed through an iterative process. Consenting students taking a course on linear regression in a Clinical and Translational Science program completed the quiz pre- and postcourse. Student results were compared to practicing statisticians with a master's or doctoral degree in statistics or a closely related field. Fifty-two students responded precourse, 59 postcourse , and 22 practicing statisticians completed the quiz. The mean (SD) score was 9.3 (4.3) for students precourse and 19.0 (3.5) postcourse (P REGRESS quiz was internally reliable (Cronbach's alpha 0.89). The initial validation is quite promising with statistically significant and meaningful differences across time and study populations. Further work is needed to validate the quiz across multiple institutions. © 2013 Wiley Periodicals, Inc.
Drzewiecki Wojciech
2016-12-01
Full Text Available In this work nine non-linear regression models were compared for sub-pixel impervious surface area mapping from Landsat images. The comparison was done in three study areas both for accuracy of imperviousness coverage evaluation in individual points in time and accuracy of imperviousness change assessment. The performance of individual machine learning algorithms (Cubist, Random Forest, stochastic gradient boosting of regression trees, k-nearest neighbors regression, random k-nearest neighbors regression, Multivariate Adaptive Regression Splines, averaged neural networks, and support vector machines with polynomial and radial kernels was also compared with the performance of heterogeneous model ensembles constructed from the best models trained using particular techniques.
A Technique of Fuzzy C-Mean in Multiple Linear Regression Model toward Paddy Yield
Syazwan Wahab, Nur; Saifullah Rusiman, Mohd; Mohamad, Mahathir; Amira Azmi, Nur; Che Him, Norziha; Ghazali Kamardan, M.; Ali, Maselan
2018-04-01
In this paper, we propose a hybrid model which is a combination of multiple linear regression model and fuzzy c-means method. This research involved a relationship between 20 variates of the top soil that are analyzed prior to planting of paddy yields at standard fertilizer rates. Data used were from the multi-location trials for rice carried out by MARDI at major paddy granary in Peninsular Malaysia during the period from 2009 to 2012. Missing observations were estimated using mean estimation techniques. The data were analyzed using multiple linear regression model and a combination of multiple linear regression model and fuzzy c-means method. Analysis of normality and multicollinearity indicate that the data is normally scattered without multicollinearity among independent variables. Analysis of fuzzy c-means cluster the yield of paddy into two clusters before the multiple linear regression model can be used. The comparison between two method indicate that the hybrid of multiple linear regression model and fuzzy c-means method outperform the multiple linear regression model with lower value of mean square error.
Anderson, Carl A; McRae, Allan F; Visscher, Peter M
2006-07-01
Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.
Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui
2014-07-01
The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.
Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs
Zuidwijk, Rob
2005-01-01
textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...
The number of subjects per variable required in linear regression analyses
P.C. Austin (Peter); E.W. Steyerberg (Ewout)
2015-01-01
textabstractObjectives To determine the number of independent variables that can be included in a linear regression model. Study Design and Setting We used a series of Monte Carlo simulations to examine the impact of the number of subjects per variable (SPV) on the accuracy of estimated regression
Tightness of M-estimators for multiple linear regression in time series
Johansen, Søren; Nielsen, Bent
We show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness requires...
Schryver, T. de; Eisinga, R.
2010-01-01
The key question in research on dismissals of head coaches in sports clubs is not whether they should happen but when they will happen. This paper applies piecewise linear regression to advance our understanding of the timing of head coach dismissals. Essentially, the regression sacrifices degrees
Invar hardening under keeping of low values of temperature coefficient of linear expansion
Bashnin, Yu.A.; Shiryaeva, A.N.; Omel'chenko, A.V.
1982-01-01
Complex invar alloying with chromium, zirconium and nitrogen is conducted for increasing hardness and assuring low values of the temperature coefficient of linear expansion. It is shown that alloying with nitride-forming elements-chromium, zirconium and the following high-temperature saturation under high pressure with nitrogen provides the invar hardening at assuring a low temperature coefficient of linear expansion. Saturation with nitrogen under 100 MPa pressure at 1050 deg C during 3 hours permits to prepare an invar containing up to 0.2% N 2 uniformly distributed over the whole cross section of samples with 4 mm diameter. Nitrogen in invar alloys alloyed with chromium and zirconium affects the Curie point similarly to carbon and nickel shifting it towards higher temperatures, it slightly changes the value of the temperature coefficient of linear expansion and provides linear character of thermal expansion dependence on temperature in the +100 deg C - -180 deg C range
Preacher, Kristopher J.; Curran, Patrick J.; Bauer, Daniel J.
2006-01-01
Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…
Investigation of linear regression of EPR dosimetric signal of the man tooth enamel
Pivovarov, S.P.; Rukhin, A.B.; Zhakparov, R.K.; Vasilevskaya, L.A.
2001-01-01
The experimental relations of the EPR radiation signal in samples of man tooth enamel of three donors of different age up to doses 1350 Gy are examined. To all of them the linear regression is applicable. The considerable errors leading to apparent non-linearity are eliminated most. (author)
Genomic prediction based on data from three layer lines using non-linear regression models
Huang, H.; Windig, J.J.; Vereijken, A.; Calus, M.P.L.
2014-01-01
Background - Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. Methods - In an attempt to alleviate
Time series linear regression of half-hourly radon levels in a residence
Hull, D.A.
1990-01-01
This paper uses time series linear regression modelling to assess the impact of temperature and pressure differences on the radon measured in the basement and in the basement drain of a research house in the Princeton area of New Jersey. The models examine half-hour averages of several climate and house parameters for several periods of up to 11 days. The drain radon concentrations follow a strong diurnal pattern that shifts 12 hours in phase between the summer and the fall seasons. This shift can be linked both to the change in temperature differences between seasons and to an experiment which involved sealing the connection between the drain and the basement. We have found that both the basement and the drain radon concentrations are correlated to basement-outdoor and soil-outdoor temperature differences (the coefficient of determination varies between 0.6 and 0.8). The statistical models for the summer periods clearly describe a physical system where the basement drain pumps radon in during the night and sucks radon out during the day
Liu Chunkui
1996-01-01
The method introduced is based on different energy of γ-ray emitted from radionuclide in the uranium-radium decay series in ore. The pulse counting rates of two spectra bands, i.e. N 1 (55∼193 keV) and N 2 (260∼1500 keV), are measured by portable type HYX-3 400-channel γ-ray spectrometer. On the other side, the uranium content (Q U ) is obtained by chemical analysis of channel sampling. Then the regression coefficients (b 0 , b 1 ,b 2 ) can be determined through dual linear regression by using Q U and N 1 , N 2 . The direct determination of uranium can be made with the regression equation Q U = b 0 + b 1 N 1 + b 2 N 2
Monopole and dipole estimation for multi-frequency sky maps by linear regression
Wehus, I. K.; Fuskeland, U.; Eriksen, H. K.; Banday, A. J.; Dickinson, C.; Ghosh, T.; Górski, K. M.; Lawrence, C. R.; Leahy, J. P.; Maino, D.; Reich, P.; Reich, W.
2017-01-01
We describe a simple but efficient method for deriving a consistent set of monopole and dipole corrections for multi-frequency sky map data sets, allowing robust parametric component separation with the same data set. The computational core of this method is linear regression between pairs of frequency maps, often called T-T plots. Individual contributions from monopole and dipole terms are determined by performing the regression locally in patches on the sky, while the degeneracy between different frequencies is lifted whenever the dominant foreground component exhibits a significant spatial spectral index variation. Based on this method, we present two different, but each internally consistent, sets of monopole and dipole coefficients for the nine-year WMAP, Planck 2013, SFD 100 μm, Haslam 408 MHz and Reich & Reich 1420 MHz maps. The two sets have been derived with different analysis assumptions and data selection, and provide an estimate of residual systematic uncertainties. In general, our values are in good agreement with previously published results. Among the most notable results are a relative dipole between the WMAP and Planck experiments of 10-15μK (depending on frequency), an estimate of the 408 MHz map monopole of 8.9 ± 1.3 K, and a non-zero dipole in the 1420 MHz map of 0.15 ± 0.03 K pointing towards Galactic coordinates (l,b) = (308°,-36°) ± 14°. These values represent the sum of any instrumental and data processing offsets, as well as any Galactic or extra-Galactic component that is spectrally uniform over the full sky.
Towards molecular design using 2D-molecular contour maps obtained from PLS regression coefficients
Borges, Cleber N.; Barigye, Stephen J.; Freitas, Matheus P.
2017-12-01
The multivariate image analysis descriptors used in quantitative structure-activity relationships are direct representations of chemical structures as they are simply numerical decodifications of pixels forming the 2D chemical images. These MDs have found great utility in the modeling of diverse properties of organic molecules. Given the multicollinearity and high dimensionality of the data matrices generated with the MIA-QSAR approach, modeling techniques that involve the projection of the data space onto orthogonal components e.g. Partial Least Squares (PLS) have been generally used. However, the chemical interpretation of the PLS-based MIA-QSAR models, in terms of the structural moieties affecting the modeled bioactivity has not been straightforward. This work describes the 2D-contour maps based on the PLS regression coefficients, as a means of assessing the relevance of single MIA predictors to the response variable, and thus allowing for the structural, electronic and physicochemical interpretation of the MIA-QSAR models. A sample study to demonstrate the utility of the 2D-contour maps to design novel drug-like molecules is performed using a dataset of some anti-HIV-1 2-amino-6-arylsulfonylbenzonitriles and derivatives, and the inferences obtained are consistent with other reports in the literature. In addition, the different schemes for encoding atomic properties in molecules are discussed and evaluated.
Varying coefficient subdistribution regression for left-truncated semi-competing risks data.
Li, Ruosha; Peng, Limin
2014-10-01
Semi-competing risks data frequently arise in biomedical studies when time to a disease landmark event is subject to dependent censoring by death, the observation of which however is not precluded by the occurrence of the landmark event. In observational studies, the analysis of such data can be further complicated by left truncation. In this work, we study a varying co-efficient subdistribution regression model for left-truncated semi-competing risks data. Our method appropriately accounts for the specifical truncation and censoring features of the data, and moreover has the flexibility to accommodate potentially varying covariate effects. The proposed method can be easily implemented and the resulting estimators are shown to have nice asymptotic properties. We also present inference, such as Kolmogorov-Smirnov type and Cramér Von-Mises type hypothesis testing procedures for the covariate effects. Simulation studies and an application to the Denmark diabetes registry demonstrate good finite-sample performance and practical utility of the proposed method.
Ng, Kar Yong; Awang, Norhashidah
2018-01-06
Frequent haze occurrences in Malaysia have made the management of PM 10 (particulate matter with aerodynamic less than 10 μm) pollution a critical task. This requires knowledge on factors associating with PM 10 variation and good forecast of PM 10 concentrations. Hence, this paper demonstrates the prediction of 1-day-ahead daily average PM 10 concentrations based on predictor variables including meteorological parameters and gaseous pollutants. Three different models were built. They were multiple linear regression (MLR) model with lagged predictor variables (MLR1), MLR model with lagged predictor variables and PM 10 concentrations (MLR2) and regression with time series error (RTSE) model. The findings revealed that humidity, temperature, wind speed, wind direction, carbon monoxide and ozone were the main factors explaining the PM 10 variation in Peninsular Malaysia. Comparison among the three models showed that MLR2 model was on a same level with RTSE model in terms of forecasting accuracy, while MLR1 model was the worst.
Song, Chao; Kwan, Mei-Po; Zhu, Jiping
2017-04-08
An increasing number of fires are occurring with the rapid development of cities, resulting in increased risk for human beings and the environment. This study compares geographically weighted regression-based models, including geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR), which integrates spatial and temporal effects and global linear regression models (LM) for modeling fire risk at the city scale. The results show that the road density and the spatial distribution of enterprises have the strongest influences on fire risk, which implies that we should focus on areas where roads and enterprises are densely clustered. In addition, locations with a large number of enterprises have fewer fire ignition records, probably because of strict management and prevention measures. A changing number of significant variables across space indicate that heterogeneity mainly exists in the northern and eastern rural and suburban areas of Hefei city, where human-related facilities or road construction are only clustered in the city sub-centers. GTWR can capture small changes in the spatiotemporal heterogeneity of the variables while GWR and LM cannot. An approach that integrates space and time enables us to better understand the dynamic changes in fire risk. Thus governments can use the results to manage fire safety at the city scale.
Derivation of linear attenuation coefficients from CT numbers for low-energy photons
Watanabe, Y.
1999-01-01
One can estimate photon attenuation properties from the CT number. In a standard method one assumes that the linear attenuation coefficient is proportional to electron density and ignores its nonlinear dependence on atomic number. When the photon energy is lower than about 50 keV, such as for brachytherapy applications, however, photoelectric absorption and Rayleigh scattering become important. Hence the atomic number must be explicitly considered in estimating the linear attenuation coefficient. In this study we propose a method to more accurately estimate the linear attenuation coefficient of low-energy photons from CT numbers. We formulate an equation that relates the CT number to the electron density and the effective atomic number. We use a CT calibration phantom to determine unknown coefficients in the equation. The equation with a given CT number is then solved for the effective atomic number, which in turn is used to calculate the linear attenuation coefficient for low-energy photons. We use the CT phantom to test the new method. The method significantly improves the standard method in estimating the attenuation coefficient at low photon energies (20keV≤E≤40keV) for materials with high atomic numbers. (author)
Vajargah, Kianoush Fathi; Sadeghi-Bazargani, Homayoun; Mehdizadeh-Esfanjani, Robab; Savadi-Oskouei, Daryoush; Farhoudi, Mehdi
2012-01-01
The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.
Two media method for linear attenuation coefficient determination of irregular soil samples
Vici, Carlos Henrique Georges
2004-01-01
In several situations of nuclear applications, the knowledge of gamma-ray linear attenuation coefficient for irregular samples is necessary, such as in soil physics and geology. This work presents the validation of a methodology for the determination of the linear attenuation coefficient (μ) of irregular shape samples, in such a way that it is not necessary to know the thickness of the considered sample. With this methodology irregular soil samples (undeformed field samples) from Londrina region, north of Parana were studied. It was employed the two media method for the μ determination. It consists of the μ determination through the measurement of a gamma-ray beam attenuation by the sample sequentially immersed in two different media, with known and appropriately chosen attenuation coefficients. For comparison, the theoretical value of μ was calculated by the product of the mass attenuation coefficient, obtained by the WinXcom code, and the measured value of the density sample. This software employs the chemical composition of the samples and supplies a table of the mass attenuation coefficients versus the photon energy. To verify the validity of the two media method, compared with the simple gamma ray transmission method, regular pome stone samples were used. With these results for the attenuation coefficients and their respective deviations, it was possible to compare the two methods. In this way we concluded that the two media method is a good tool for the determination of the linear attenuation coefficient of irregular materials, particularly in the study of soils samples. (author)
Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method
Seçil YALAZ
2016-10-01
Full Text Available Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models’ degree. Changing the models’ degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT and to estimate future an equation has created by applying fuzzy least square regression (FLSR method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study. In conclusion, to demonstrate our methods’ efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures.
Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs
R.A. Zuidwijk (Rob)
2005-01-01
textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an
Carausu, A.
1996-01-01
A method for the fragility estimation of seismically isolated nuclear power plant structure is proposed. The relationship between the ground motion intensity parameter (e.g. peak ground velocity or peak ground acceleration) and the response of isolated structures is expressed in terms of a bi-linear regression line, whose coefficients are estimated by the least-square method in terms of available data on seismic input and structural response. The notion of high confidence low probability of failure (HCLPF) value is also used for deriving compound fragility curves for coupled subsystems. (orig.)
Xu, Jiucheng; Mu, Huiyu; Wang, Yun; Huang, Fangzhou
2018-01-01
The selection of feature genes with high recognition ability from the gene expression profiles has gained great significance in biology. However, most of the existing methods have a high time complexity and poor classification performance. Motivated by this, an effective feature selection method, called supervised locally linear embedding and Spearman's rank correlation coefficient (SLLE-SC 2 ), is proposed which is based on the concept of locally linear embedding and correlation coefficient algorithms. Supervised locally linear embedding takes into account class label information and improves the classification performance. Furthermore, Spearman's rank correlation coefficient is used to remove the coexpression genes. The experiment results obtained on four public tumor microarray datasets illustrate that our method is valid and feasible.
Measurements of linear attenuation coefficients of irregular shaped samples by two media method
Singh, Sukhpal; Kumar, Ashok; Thind, Kulwant Singh; Mudahar, Gurmel S.
2008-01-01
The linear attenuation coefficient values of regular and irregular shaped flyash materials have been measured without knowing the thickness of a sample using a new technique namely 'two media method'. These values have also been measured with a standard gamma ray transmission method and obtained theoretically with winXCOM computer code. From the comparison it is reported that the two media method has given accurate results of attenuation coefficients of flyash materials
Fang, Tingting; Lahdelma, Risto
2016-01-01
Highlights: • Social factor is considered for the linear regression models besides weather file. • Simultaneously optimize all the coefficients for linear regression models. • SARIMA combined with linear regression is used to forecast the heat demand. • The accuracy for both linear regression and time series models are evaluated. - Abstract: Forecasting heat demand is necessary for production and operation planning of district heating (DH) systems. In this study we first propose a simple regression model where the hourly outdoor temperature and wind speed forecast the heat demand. Weekly rhythm of heat consumption as a social component is added to the model to significantly improve the accuracy. The other type of model is the seasonal autoregressive integrated moving average (SARIMA) model with exogenous variables as a combination to take weather factors, and the historical heat consumption data as depending variables. One outstanding advantage of the model is that it peruses the high accuracy for both long-term and short-term forecast by considering both exogenous factors and time series. The forecasting performance of both linear regression models and time series model are evaluated based on real-life heat demand data for the city of Espoo in Finland by out-of-sample tests for the last 20 full weeks of the year. The results indicate that the proposed linear regression model (T168h) using 168-h demand pattern with midweek holidays classified as Saturdays or Sundays gives the highest accuracy and strong robustness among all the tested models based on the tested forecasting horizon and corresponding data. Considering the parsimony of the input, the ease of use and the high accuracy, the proposed T168h model is the best in practice. The heat demand forecasting model can also be developed for individual buildings if automated meter reading customer measurements are available. This would allow forecasting the heat demand based on more accurate heat consumption
Meaney, Christopher; Moineddin, Rahim
2014-01-24
In biomedical research, response variables are often encountered which have bounded support on the open unit interval--(0,1). Traditionally, researchers have attempted to estimate covariate effects on these types of response data using linear regression. Alternative modelling strategies may include: beta regression, variable-dispersion beta regression, and fractional logit regression models. This study employs a Monte Carlo simulation design to compare the statistical properties of the linear regression model to that of the more novel beta regression, variable-dispersion beta regression, and fractional logit regression models. In the Monte Carlo experiment we assume a simple two sample design. We assume observations are realizations of independent draws from their respective probability models. The randomly simulated draws from the various probability models are chosen to emulate average proportion/percentage/rate differences of pre-specified magnitudes. Following simulation of the experimental data we estimate average proportion/percentage/rate differences. We compare the estimators in terms of bias, variance, type-1 error and power. Estimates of Monte Carlo error associated with these quantities are provided. If response data are beta distributed with constant dispersion parameters across the two samples, then all models are unbiased and have reasonable type-1 error rates and power profiles. If the response data in the two samples have different dispersion parameters, then the simple beta regression model is biased. When the sample size is small (N0 = N1 = 25) linear regression has superior type-1 error rates compared to the other models. Small sample type-1 error rates can be improved in beta regression models using bias correction/reduction methods. In the power experiments, variable-dispersion beta regression and fractional logit regression models have slightly elevated power compared to linear regression models. Similar results were observed if the
Zhao, Yu Xi; Xie, Ping; Sang, Yan Fang; Wu, Zi Yi
2018-04-01
Hydrological process evaluation is temporal dependent. Hydrological time series including dependence components do not meet the data consistency assumption for hydrological computation. Both of those factors cause great difficulty for water researches. Given the existence of hydrological dependence variability, we proposed a correlationcoefficient-based method for significance evaluation of hydrological dependence based on auto-regression model. By calculating the correlation coefficient between the original series and its dependence component and selecting reasonable thresholds of correlation coefficient, this method divided significance degree of dependence into no variability, weak variability, mid variability, strong variability, and drastic variability. By deducing the relationship between correlation coefficient and auto-correlation coefficient in each order of series, we found that the correlation coefficient was mainly determined by the magnitude of auto-correlation coefficient from the 1 order to p order, which clarified the theoretical basis of this method. With the first-order and second-order auto-regression models as examples, the reasonability of the deduced formula was verified through Monte-Carlo experiments to classify the relationship between correlation coefficient and auto-correlation coefficient. This method was used to analyze three observed hydrological time series. The results indicated the coexistence of stochastic and dependence characteristics in hydrological process.
Integral linear momentum balance in combining flows for calculating the pressure drop coefficients
Bollmann, A.
1983-01-01
Equations for calculating the loss coefficient in combining flows in tee functions are obtained by an integral linear momentum balance. It is a practice, when solving this type of problem, to neglect the pressure difference in the upstream location as well as the wall-fluid interaction in the lateral branch of the junction. In this work it is demonstrated the influence of the above parameters on the loss coefficient based on experimental values and by apropriate algebraic manipulation of the loss coefficient values published by previous investigators. (Author) [pt
Bini, L. M.; Diniz-Filho, J. A. F.; Rangel, T. F. L. V. B.
2009-01-01
A major focus of geographical ecology and macroecology is to understand the causes of spatially structured ecological patterns. However, achieving this understanding can be complicated when using multiple regression, because the relative importance of explanatory variables, as measured by regress...
Bonellie, Sandra R
2012-10-01
To illustrate the use of regression and logistic regression models to investigate changes over time in size of babies particularly in relation to social deprivation, age of the mother and smoking. Mean birthweight has been found to be increasing in many countries in recent years, but there are still a group of babies who are born with low birthweights. Population-based retrospective cohort study. Multiple linear regression and logistic regression models are used to analyse data on term 'singleton births' from Scottish hospitals between 1994-2003. Mothers who smoke are shown to give birth to lighter babies on average, a difference of approximately 0.57 Standard deviations lower (95% confidence interval. 0.55-0.58) when adjusted for sex and parity. These mothers are also more likely to have babies that are low birthweight (odds ratio 3.46, 95% confidence interval 3.30-3.63) compared with non-smokers. Low birthweight is 30% more likely where the mother lives in the most deprived areas compared with the least deprived, (odds ratio 1.30, 95% confidence interval 1.21-1.40). Smoking during pregnancy is shown to have a detrimental effect on the size of infants at birth. This effect explains some, though not all, of the observed socioeconomic birthweight. It also explains much of the observed birthweight differences by the age of the mother. Identifying mothers at greater risk of having a low birthweight baby as important implications for the care and advice this group receives. © 2012 Blackwell Publishing Ltd.
Treating experimental data of inverse kinetic method by unitary linear regression analysis
Zhao Yusen; Chen Xiaoliang
2009-01-01
The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)
Model structure learning: A support vector machine approach for LPV linear-regression models
Toth, R.; Laurain, V.; Zheng, W-X.; Poolla, K.
2011-01-01
Accurate parametric identification of Linear Parameter-Varying (LPV) systems requires an optimal prior selection of a set of functional dependencies for the parametrization of the model coefficients. Inaccurate selection leads to structural bias while over-parametrization results in a variance
Zhou, X; Zhang, Z Y; Zhang, Q M; Liu, Q; Ding, Y Y; Zhou, L; Cao, J
2015-01-01
We report the measurements of the densities of linear alkylbenzene at three temperatures over 4 to 23 °C with pressures up to 10 MPa. The measurements have been analysed to yield the isobaric thermal expansion coefficients and, so far for the first time, isothermal compressibilities of linear alkylbenzene. Relevance of results for current generation (i.e., Daya Bay) and next generation (i.e. JUNO) large liquid scintillator neutrino detectors are discussed. (paper)
Materials analysis using x-ray linear attenuation coefficient measurements at four photon energies
Midgley, S M
2005-01-01
The analytical properties of an accurate parameterization scheme for the x-ray linear attenuation coefficient are examined. The parameterization utilizes an additive combination of N compositional- and energy-dependent coefficients. The former were derived from a parameterization of elemental cross-sections using a polynomial in atomic number. The compositional-dependent coefficients are referred to as the mixture parameters, representing the electron density and higher order statistical moments describing elemental distribution. Additivity is an important property of the parameterization, allowing measured x-ray linear attenuation coefficients to be written as linear simultaneous equations, and then solved for the unknown coefficients. The energy-dependent coefficients can be determined by calibration from measurements with materials of known composition. The inverse problem may be utilized for materials analysis, whereby the simultaneous equations represent multi-energy linear attenuation coefficient measurements, and are solved for the mixture parameters. For in vivo studies, the choice of measurement energies is restricted to the diagnostic region (approximately 20 keV to 150 keV), where the parameterization requires N ≥ 4 energies. We identify a mathematical pathology that must be overcome in order to solve the inverse problem in this energy regime. An iterative inversion strategy is presented for materials analysis using four or more measurements, and then tested against real data obtained at energies 32 keV to 66 keV. The results demonstrate that it is possible to recover the electron density to within ±4% and fourth mixture parameter. It is also a key finding that the second and third mixture parameters cannot be recovered, as they are of minor importance in the parameterization at diagnostic x-ray energies
Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
Freund, Roland
1989-01-01
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Akbari, Somaye; Zebardast, Tannaz; Zarghi, Afshin; Hajimahdi, Zahra
2017-01-01
COX-2 inhibitory activities of some 1,4-dihydropyridine and 5-oxo-1,4,5,6,7,8-hexahydroquinoline derivatives were modeled by quantitative structure-activity relationship (QSAR) using stepwise-multiple linear regression (SW-MLR) method. The built model was robust and predictive with correlation coefficient (R 2 ) of 0.972 and 0.531 for training and test groups, respectively. The quality of the model was evaluated by leave-one-out (LOO) cross validation (LOO correlation coefficient (Q 2 ) of 0.943) and Y-randomization. We also employed a leverage approach for the defining of applicability domain of model. Based on QSAR models results, COX-2 inhibitory activity of selected data set had correlation with BEHm6 (highest eigenvalue n. 6 of Burden matrix/weighted by atomic masses), Mor03u (signal 03/unweighted) and IVDE (Mean information content on the vertex degree equality) descriptors which derived from their structures.
The Relationship between Economic Growth and Money Laundering – a Linear Regression Model
Daniel Rece
2009-09-01
Full Text Available This study provides an overview of the relationship between economic growth and money laundering modeled by a least squares function. The report analyzes statistically data collected from USA, Russia, Romania and other eleven European countries, rendering a linear regression model. The study illustrates that 23.7% of the total variance in the regressand (level of money laundering is “explained” by the linear regression model. In our opinion, this model will provide critical auxiliary judgment and decision support for anti-money laundering service systems.
Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F
2018-03-26
This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.
Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M
2013-01-01
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.
Liyun Su
2012-01-01
Full Text Available We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations.
Using the classical linear regression model in analysis of the dependences of conveyor belt life
Miriam Andrejiová
2013-12-01
Full Text Available The paper deals with the classical linear regression model of the dependence of conveyor belt life on some selected parameters: thickness of paint layer, width and length of the belt, conveyor speed and quantity of transported material. The first part of the article is about regression model design, point and interval estimation of parameters, verification of statistical significance of the model, and about the parameters of the proposed regression model. The second part of the article deals with identification of influential and extreme values that can have an impact on estimation of regression model parameters. The third part focuses on assumptions of the classical regression model, i.e. on verification of independence assumptions, normality and homoscedasticity of residuals.
Modeling of Soil Aggregate Stability using Support Vector Machines and Multiple Linear Regression
Ali Asghar Besalatpour
2016-02-01
by 20-m digital elevation model (DEM. The data set was divided into two subsets of training and testing. The training subset was randomly chosen from 70% of the total set of the data and the remaining samples (30% of the data were used as the testing set. The correlation coefficient (r, mean square error (MSE, and error percentage (ERROR% between the measured and the predicted GMD values were used to evaluate the performance of the models. Results and Discussion: The description statistics showed that there was little variability in the sample distributions of the variables used in this study to develop the GMD prediction models, indicating that their values were all normally distributed. The constructed SVM model had better performance in predicting GMD compared to the traditional multiple linear regression model. The obtained MSE and r values for the developed SVM model for soil aggregate stability prediction were 0.005 and 0.86, respectively. The obtained ERROR% value for soil aggregate stability prediction using the SVM model was 10.7% while it was 15.7% for the regression model. The scatter plot figures also showed that the SVM model was more accurate in GMD estimation than the MLR model, since the predicted GMD values were closer in agreement with the measured values for most of the samples. The worse performance of the MLR model might be due to the larger amount of data that is required for developing a sustainable regression model compared to intelligent systems. Furthermore, only the linear effects of the predictors on the dependent variable can be extracted by linear models while in many cases the effects may not be linear in nature. Meanwhile, the SVM model is suitable for modelling nonlinear relationships and its major advantage is that the method can be developed without knowing the exact form of the analytical function on which the model should be built. All these indicate that the SVM approach would be a better choice for predicting soil aggregate
Regression of non-linear coupling of noise in LIGO detectors
Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.
2018-03-01
In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.
Peng Jiang
2013-01-01
Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.
A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants
Cooper, Paul D.
2010-01-01
A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…
Thompson, Russel L.
Homoscedasticity is an important assumption of linear regression. This paper explains what it is and why it is important to the researcher. Graphical and mathematical methods for testing the homoscedasticity assumption are demonstrated. Sources of homoscedasticity and types of homoscedasticity are discussed, and methods for correction are…
Due to the complexity of the processes contributing to beach bacteria concentrations, many researchers rely on statistical modeling, among which multiple linear regression (MLR) modeling is most widely used. Despite its ease of use and interpretation, there may be time dependence...
Application of range-test in multiple linear regression analysis in ...
Application of range-test in multiple linear regression analysis in the presence of outliers is studied in this paper. First, the plot of the explanatory variables (i.e. Administration, Social/Commercial, Economic services and Transfer) on the dependent variable (i.e. GDP) was done to identify the statistical trend over the years.
Ling, Ru; Liu, Jiawang
2011-12-01
To construct prediction model for health workforce and hospital beds in county hospitals of Hunan by multiple linear regression. We surveyed 16 counties in Hunan with stratified random sampling according to uniform questionnaires,and multiple linear regression analysis with 20 quotas selected by literature view was done. Independent variables in the multiple linear regression model on medical personnels in county hospitals included the counties' urban residents' income, crude death rate, medical beds, business occupancy, professional equipment value, the number of devices valued above 10 000 yuan, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, and utilization rate of hospital beds. Independent variables in the multiple linear regression model on county hospital beds included the the population of aged 65 and above in the counties, disposable income of urban residents, medical personnel of medical institutions in county area, business occupancy, the total value of professional equipment, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, utilization rate of hospital beds, and length of hospitalization. The prediction model shows good explanatory and fitting, and may be used for short- and mid-term forecasting.
Walter, G.M.; Augustin, Th.; Kneib, Thomas; Tutz, Gerhard
2010-01-01
The paper is concerned with Bayesian analysis under prior-data conflict, i.e. the situation when observed data are rather unexpected under the prior (and the sample size is not large enough to eliminate the influence of the prior). Two approaches for Bayesian linear regression modeling based on
Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp
We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...
Giuliano de Oliveira Freitas
2013-10-01
Full Text Available PURPOSE: To determine linear regression models between Alpins descriptive indices and Thibos astigmatic power vectors (APV, assessing the validity and strength of such correlations. METHODS: This case series prospectively assessed 62 eyes of 31 consecutive cataract patients with preoperative corneal astigmatism between 0.75 and 2.50 diopters in both eyes. Patients were randomly assorted among two phacoemulsification groups: one assigned to receive AcrySof®Toric intraocular lens (IOL in both eyes and another assigned to have AcrySof Natural IOL associated with limbal relaxing incisions, also in both eyes. All patients were reevaluated postoperatively at 6 months, when refractive astigmatism analysis was performed using both Alpins and Thibos methods. The ratio between Thibos postoperative APV and preoperative APV (APVratio and its linear regression to Alpins percentage of success of astigmatic surgery, percentage of astigmatism corrected and percentage of astigmatism reduction at the intended axis were assessed. RESULTS: Significant negative correlation between the ratio of post- and preoperative Thibos APVratio and Alpins percentage of success (%Success was found (Spearman's ρ=-0.93; linear regression is given by the following equation: %Success = (-APVratio + 1.00x100. CONCLUSION: The linear regression we found between APVratio and %Success permits a validated mathematical inference concerning the overall success of astigmatic surgery.
Power properties of invariant tests for spatial autocorrelation in linear regression
Martellosio, F.
2006-01-01
Many popular tests for residual spatial autocorrelation in the context of the linear regression model belong to the class of invariant tests. This paper derives a number of exact properties of the power function of such tests. In particular, we extend the work of Krämer (2005, Journal of Statistical
Khalil, Mohamed H; Shebl, Mostafa K; Kosba, Mohamed A; El-Sabrout, Karim; Zaki, Nesma
2016-08-01
This research was conducted to determine the most affecting parameters on hatchability of indigenous and improved local chickens' eggs. Five parameters were studied (fertility, early and late embryonic mortalities, shape index, egg weight, and egg weight loss) on four strains, namely Fayoumi, Alexandria, Matrouh, and Montazah. Multiple linear regression was performed on the studied parameters to determine the most influencing one on hatchability. The results showed significant differences in commercial and scientific hatchability among strains. Alexandria strain has the highest significant commercial hatchability (80.70%). Regarding the studied strains, highly significant differences in hatching chick weight among strains were observed. Using multiple linear regression analysis, fertility made the greatest percent contribution (71.31%) to hatchability, and the lowest percent contributions were made by shape index and egg weight loss. A prediction of hatchability using multiple regression analysis could be a good tool to improve hatchability percentage in chickens.
truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models
Maria Karlsson
2014-05-01
Full Text Available Problems with truncated data occur in many areas, complicating estimation and inference. Regarding linear regression models, the ordinary least squares estimator is inconsistent and biased for these types of data and is therefore unsuitable for use. Alternative estimators, designed for the estimation of truncated regression models, have been developed. This paper presents the R package truncSP. The package contains functions for the estimation of semi-parametric truncated linear regression models using three different estimators: the symmetrically trimmed least squares, quadratic mode, and left truncated estimators, all of which have been shown to have good asymptotic and ?nite sample properties. The package also provides functions for the analysis of the estimated models. Data from the environmental sciences are used to illustrate the functions in the package.
Genomic prediction based on data from three layer lines using non-linear regression models.
Huang, Heyun; Windig, Jack J; Vereijken, Addie; Calus, Mario P L
2014-11-06
Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values. When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction. Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional
Single image super-resolution using locally adaptive multiple linear regression.
Yu, Soohwan; Kang, Wonseok; Ko, Seungyong; Paik, Joonki
2015-12-01
This paper presents a regularized superresolution (SR) reconstruction method using locally adaptive multiple linear regression to overcome the limitation of spatial resolution of digital images. In order to make the SR problem better-posed, the proposed method incorporates the locally adaptive multiple linear regression into the regularization process as a local prior. The local regularization prior assumes that the target high-resolution (HR) pixel is generated by a linear combination of similar pixels in differently scaled patches and optimum weight parameters. In addition, we adapt a modified version of the nonlocal means filter as a smoothness prior to utilize the patch redundancy. Experimental results show that the proposed algorithm better restores HR images than existing state-of-the-art methods in the sense of the most objective measures in the literature.
Suzuki, Makoto; Sugimura, Yuko; Yamada, Sumio; Omori, Yoshitsugu; Miyamoto, Masaaki; Yamamoto, Jun-ichi
2013-01-01
Cognitive disorders in the acute stage of stroke are common and are important independent predictors of adverse outcome in the long term. Despite the impact of cognitive disorders on both patients and their families, it is still difficult to predict the extent or duration of cognitive impairments. The objective of the present study was, therefore, to provide data on predicting the recovery of cognitive function soon after stroke by differential modeling with logarithmic and linear regression. This study included two rounds of data collection comprising 57 stroke patients enrolled in the first round for the purpose of identifying the time course of cognitive recovery in the early-phase group data, and 43 stroke patients in the second round for the purpose of ensuring that the correlation of the early-phase group data applied to the prediction of each individual's degree of cognitive recovery. In the first round, Mini-Mental State Examination (MMSE) scores were assessed 3 times during hospitalization, and the scores were regressed on the logarithm and linear of time. In the second round, calculations of MMSE scores were made for the first two scoring times after admission to tailor the structures of logarithmic and linear regression formulae to fit an individual's degree of functional recovery. The time course of early-phase recovery for cognitive functions resembled both logarithmic and linear functions. However, MMSE scores sampled at two baseline points based on logarithmic regression modeling could estimate prediction of cognitive recovery more accurately than could linear regression modeling (logarithmic modeling, R(2) = 0.676, PLogarithmic modeling based on MMSE scores could accurately predict the recovery of cognitive function soon after the occurrence of stroke. This logarithmic modeling with mathematical procedures is simple enough to be adopted in daily clinical practice.
Yu, Xu; Lin, Jun-Yu; Jiang, Feng; Du, Jun-Wei; Han, Ji-Zhong
2018-01-01
Cross-domain collaborative filtering (CDCF) solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR). We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR) model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods.
Xu Yu
2018-01-01
Full Text Available Cross-domain collaborative filtering (CDCF solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR. We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods.
Drzewiecki, Wojciech
2016-12-01
In this work nine non-linear regression models were compared for sub-pixel impervious surface area mapping from Landsat images. The comparison was done in three study areas both for accuracy of imperviousness coverage evaluation in individual points in time and accuracy of imperviousness change assessment. The performance of individual machine learning algorithms (Cubist, Random Forest, stochastic gradient boosting of regression trees, k-nearest neighbors regression, random k-nearest neighbors regression, Multivariate Adaptive Regression Splines, averaged neural networks, and support vector machines with polynomial and radial kernels) was also compared with the performance of heterogeneous model ensembles constructed from the best models trained using particular techniques. The results proved that in case of sub-pixel evaluation the most accurate prediction of change may not necessarily be based on the most accurate individual assessments. When single methods are considered, based on obtained results Cubist algorithm may be advised for Landsat based mapping of imperviousness for single dates. However, Random Forest may be endorsed when the most reliable evaluation of imperviousness change is the primary goal. It gave lower accuracies for individual assessments, but better prediction of change due to more correlated errors of individual predictions. Heterogeneous model ensembles performed for individual time points assessments at least as well as the best individual models. In case of imperviousness change assessment the ensembles always outperformed single model approaches. It means that it is possible to improve the accuracy of sub-pixel imperviousness change assessment using ensembles of heterogeneous non-linear regression models.
Analysis of dental caries using generalized linear and count regression models
Javali M. Phil
2013-11-01
Full Text Available Generalized linear models (GLM are generalization of linear regression models, which allow fitting regression models to response data in all the sciences especially medical and dental sciences that follow a general exponential family. These are flexible and widely used class of such models that can accommodate response variables. Count data are frequently characterized by overdispersion and excess zeros. Zero-inflated count models provide a parsimonious yet powerful way to model this type of situation. Such models assume that the data are a mixture of two separate data generation processes: one generates only zeros, and the other is either a Poisson or a negative binomial data-generating process. Zero inflated count regression models such as the zero-inflated Poisson (ZIP, zero-inflated negative binomial (ZINB regression models have been used to handle dental caries count data with many zeros. We present an evaluation framework to the suitability of applying the GLM, Poisson, NB, ZIP and ZINB to dental caries data set where the count data may exhibit evidence of many zeros and over-dispersion. Estimation of the model parameters using the method of maximum likelihood is provided. Based on the Vuong test statistic and the goodness of fit measure for dental caries data, the NB and ZINB regression models perform better than other count regression models.
Zhang, Yanyan; Ma, Haile; Wang, Bei; Qu, Wenjuan; Wali, Asif; Zhou, Cunshan
2016-08-01
Ultrasound pretreatment of wheat gluten (WG) before enzymolysis can improve the angiotensin converting enzyme (ACE) inhibitory activity of the hydrolysates by alerting the structure of substrate proteins. Establishment of a relationship between the structure of WG and ACE inhibitory activity of the hydrolysates to judge the end point of the ultrasonic pretreatment is vital. The results of stepwise multiple linear regression (MLR) showed that the contents of free sulfhydryl, α-helix, disulfide bond, surface hydrophobicity and random coil were significantly correlated to ACE Inhibitory activity of the hydrolysate, with the standard partial regression coefficients were 3.729, -0.676, -0.252, 0.022 and 0.156, respectively. The R(2) of this model was 0.970. External validation showed that the stepwise MLR model could well predict the ACE inhibitory activity of hydrolysate based on the content of free sulfhydryl, α-helix, disulfide bond, surface hydrophobicity and random coil of WG before hydrolysis. A stepwise multiple linear regression model describing the quantitative relationships between the structure of WG and the ACE Inhibitory activity of the hydrolysates was established. This model can be used to predict the endpoint of the ultrasonic pretreatment. © 2015 Society of Chemical Industry. © 2015 Society of Chemical Industry.
C. Wu
2018-03-01
Full Text Available Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS, Deming regression (DR, orthogonal distance regression (ODR, weighted ODR (WODR, and York regression (YR. We first introduce a new data generation scheme that employs the Mersenne twister (MT pseudorandom number generator. The numerical simulations are also improved by (a refining the parameterization of nonlinear measurement uncertainties, (b inclusion of a linear measurement uncertainty, and (c inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot was developed to facilitate the implementation of error-in-variables regressions.
Wu, Cheng; Zhen Yu, Jian
2018-03-01
Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.
System of coefficients for charged-particle beam linear transformation by a magnetic dipole element
Tarantin, N.I.
1979-01-01
A new technique for consideration of dipole magnet ion-optical effect has been developed to study the problems of commutation and monochromatization of a charged particle beam. In a new form obtained are systematized coefficients of linear transformation (CLT) of the charged particle beam for radial and axial motions in a magnetic dipole element (MDE) including a dipole magnet and two gaps without magnetic field. Given is a method of graphic determination of MDE parameters and main CLT. The new form of coefficients and conditions of the transformations feasibility considerably facilitates the choice and calculation of dipole elements
Yue, Chen; Chen, Shaojie; Sair, Haris I; Airan, Raag; Caffo, Brian S
2015-09-01
Data reproducibility is a critical issue in all scientific experiments. In this manuscript, the problem of quantifying the reproducibility of graphical measurements is considered. The image intra-class correlation coefficient (I2C2) is generalized and the graphical intra-class correlation coefficient (GICC) is proposed for such purpose. The concept for GICC is based on multivariate probit-linear mixed effect models. A Markov Chain Monte Carlo EM (mcm-cEM) algorithm is used for estimating the GICC. Simulation results with varied settings are demonstrated and our method is applied to the KIRBY21 test-retest dataset.
MCKissick, Burnell T. (Technical Monitor); Plassman, Gerald E.; Mall, Gerald H.; Quagliano, John R.
2005-01-01
Linear multivariable regression models for predicting day and night Eddy Dissipation Rate (EDR) from available meteorological data sources are defined and validated. Model definition is based on a combination of 1997-2000 Dallas/Fort Worth (DFW) data sources, EDR from Aircraft Vortex Spacing System (AVOSS) deployment data, and regression variables primarily from corresponding Automated Surface Observation System (ASOS) data. Model validation is accomplished through EDR predictions on a similar combination of 1994-1995 Memphis (MEM) AVOSS and ASOS data. Model forms include an intercept plus a single term of fixed optimal power for each of these regression variables; 30-minute forward averaged mean and variance of near-surface wind speed and temperature, variance of wind direction, and a discrete cloud cover metric. Distinct day and night models, regressing on EDR and the natural log of EDR respectively, yield best performance and avoid model discontinuity over day/night data boundaries.
A method for fitting regression splines with varying polynomial order in the linear mixed model.
Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W
2006-02-15
The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.
Linear thermal expansion coefficient of MgAl2O4(s)
Dash, A.; Samui, P.; Naik, Y.P.; Chaudhary, Z.S.
2011-01-01
The coefficient of linear thermal expansion (α av ) of MgAl 2 O 4 (s) has been determined using a Netzsch 402 PC dilatometer with Al 2 O 3 (s) as the push-rod. The change in length per unit length was recorded as a function of temperature between room temperature to 1273 K at a heating rate of 8 K.min /1 , in argon flowing atmosphere. The average of three measurements was quoted as the α av for MgAl 2 O 4 (s). The linear thermal expansion was measured to an accuracy of ±3%. (author)
Linear regression analysis: part 14 of a series on evaluation of scientific publications.
Schneider, Astrid; Hommel, Gerhard; Blettner, Maria
2010-11-01
Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the results should be interpreted. The reader should then be able to judge whether the method has been used correctly and interpret the results appropriately. The performance and interpretation of linear regression analysis are subject to a variety of pitfalls, which are discussed here in detail. The reader is made aware of common errors of interpretation through practical examples. Both the opportunities for applying linear regression analysis and its limitations are presented.
A Compensatory Approach to Multiobjective Linear Transportation Problem with Fuzzy Cost Coefficients
Hale Gonce Kocken
2011-01-01
Full Text Available This paper deals with the Multiobjective Linear Transportation Problem that has fuzzy cost coefficients. In the solution procedure, many objectives may conflict with each other; therefore decision-making process becomes complicated. And also due to the fuzziness in the costs, this problem has a nonlinear structure. In this paper, fuzziness in the objective functions is handled with a fuzzy programming technique in the sense of multiobjective approach. And then we present a compensatory approach to solve Multiobjective Linear Transportation Problem with fuzzy cost coefficients by using Werner's and operator. Our approach generates compromise solutions which are both compensatory and Pareto optimal. A numerical example has been provided to illustrate the problem.
The linear attenuation coefficients as features of multiple energy CT image classification
Homem, M.R.P.; Mascarenhas, N.D.A.; Cruvinel, P.E.
2000-01-01
We present in this paper an analysis of the linear attenuation coefficients as useful features of single and multiple energy CT images with the use of statistical pattern classification tools. We analyzed four CT images through two pointwise classifiers (the first classifier is based on the maximum-likelihood criterion and the second classifier is based on the k-means clustering algorithm) and one contextual Bayesian classifier (ICM algorithm - Iterated Conditional Modes) using an a priori Potts-Strauss model. A feature extraction procedure using the Jeffries-Matusita (J-M) distance and the Karhunen-Loeve transformation was also performed. Both the classification and the feature selection procedures were found to be in agreement with the predicted discrimination given by the separation of the linear attenuation coefficient curves for different materials
METİN KAMİL ERCAN
2013-06-01
Full Text Available It is possible to determine the value of private companies by means of suggestions and assumptions derived from their financial statements. However, there comes out a serious problem in the determination of equity costs of these private companies using Capital Assets Pricing Model (CAPM as beta coefficients are unknown or unavailable. In this study, firstly, a regression model that represents the relationship between the beta coefficients and financial statements’ Variables of publicly-held companies will be developed. Then, this model will be tested and applied on private companies.
Linear Regression on Sparse Features for Single-Channel Speech Separation
Schmidt, Mikkel N.; Olsson, Rasmus Kongsgaard
2007-01-01
In this work we address the problem of separating multiple speakers from a single microphone recording. We formulate a linear regression model for estimating each speaker based on features derived from the mixture. The employed feature representation is a sparse, non-negative encoding of the speech...... mixture in terms of pre-learned speaker-dependent dictionaries. Previous work has shown that this feature representation by itself provides some degree of separation. We show that the performance is significantly improved when regression analysis is performed on the sparse, non-negative features, both...
Prediction of Mind-Wandering with Electroencephalogram and Non-linear Regression Modeling.
Kawashima, Issaku; Kumano, Hiroaki
2017-01-01
Mind-wandering (MW), task-unrelated thought, has been examined by researchers in an increasing number of articles using models to predict whether subjects are in MW, using numerous physiological variables. However, these models are not applicable in general situations. Moreover, they output only binary classification. The current study suggests that the combination of electroencephalogram (EEG) variables and non-linear regression modeling can be a good indicator of MW intensity. We recorded EEGs of 50 subjects during the performance of a Sustained Attention to Response Task, including a thought sampling probe that inquired the focus of attention. We calculated the power and coherence value and prepared 35 patterns of variable combinations and applied Support Vector machine Regression (SVR) to them. Finally, we chose four SVR models: two of them non-linear models and the others linear models; two of the four models are composed of a limited number of electrodes to satisfy model usefulness. Examination using the held-out data indicated that all models had robust predictive precision and provided significantly better estimations than a linear regression model using single electrode EEG variables. Furthermore, in limited electrode condition, non-linear SVR model showed significantly better precision than linear SVR model. The method proposed in this study helps investigations into MW in various little-examined situations. Further, by measuring MW with a high temporal resolution EEG, unclear aspects of MW, such as time series variation, are expected to be revealed. Furthermore, our suggestion that a few electrodes can also predict MW contributes to the development of neuro-feedback studies.
Prediction of Mind-Wandering with Electroencephalogram and Non-linear Regression Modeling
Issaku Kawashima
2017-07-01
Full Text Available Mind-wandering (MW, task-unrelated thought, has been examined by researchers in an increasing number of articles using models to predict whether subjects are in MW, using numerous physiological variables. However, these models are not applicable in general situations. Moreover, they output only binary classification. The current study suggests that the combination of electroencephalogram (EEG variables and non-linear regression modeling can be a good indicator of MW intensity. We recorded EEGs of 50 subjects during the performance of a Sustained Attention to Response Task, including a thought sampling probe that inquired the focus of attention. We calculated the power and coherence value and prepared 35 patterns of variable combinations and applied Support Vector machine Regression (SVR to them. Finally, we chose four SVR models: two of them non-linear models and the others linear models; two of the four models are composed of a limited number of electrodes to satisfy model usefulness. Examination using the held-out data indicated that all models had robust predictive precision and provided significantly better estimations than a linear regression model using single electrode EEG variables. Furthermore, in limited electrode condition, non-linear SVR model showed significantly better precision than linear SVR model. The method proposed in this study helps investigations into MW in various little-examined situations. Further, by measuring MW with a high temporal resolution EEG, unclear aspects of MW, such as time series variation, are expected to be revealed. Furthermore, our suggestion that a few electrodes can also predict MW contributes to the development of neuro-feedback studies.
Zhang, Richard X; Fisher, Timothy; Raman, Arvind; Sands, Timothy D
2009-01-01
In this article, a precise and convenient technique based on the atomic force microscope (AFM) is developed to measure the linear coefficient of thermal expansion of a porous anodic alumina thin film. A stage was used to heat the sample from room temperature up to 450 K. Thermal effects on AFM probes and different operation modes at elevated temperatures were also studied, and a silicon AFM probe in the tapping mode was chosen for the subsequent measurements due to its temperature insensitivi...
V. S. Zarubin
2015-01-01
Full Text Available The rational use of composites as structural materials, while perceiving the thermal and mechanical loads, to a large extent determined by their thermoelastic properties. From the presented review of works devoted to the analysis of thermoelastic characteristics of composites, it follows that the problem of estimating these characteristics is important. Among the thermoelastic properties of composites occupies an important place its temperature coefficient of linear expansion.Along with fiber composites are widely used in the technique of dispersion hardening composites, in which the role of inclusions carry particles of high-strength and high-modulus materials, including nanostructured elements. Typically, the dispersed particles have similar dimensions in all directions, which allows the shape of the particles in the first approximation the ball.In an article for the composite with isotropic spherical inclusions of a plurality of different materials by the self-produced design formulas relating the temperature coefficient of linear expansion with volume concentration of inclusions and their thermoelastic characteristics, as well as the thermoelastic properties of the matrix of the composite. Feature of the method is the self-accountability thermomechanical interaction of a single inclusion or matrix particles with a homogeneous isotropic medium having the desired temperature coefficient of linear expansion. Averaging over the volume of the composite arising from such interaction perturbation strain and stress in the inclusions and the matrix particles and makes it possible to obtain such calculation formulas.For the validation of the results of calculations of the temperature coefficient of linear expansion of the composite of this type used two-sided estimates that are based on the dual variational formulation of linear thermoelasticity problem in an inhomogeneous solid containing two alternative functional (such as Lagrange and Castigliano
Liu, Yan; Salvendy, Gavriel
2009-05-01
This paper aims to demonstrate the effects of measurement errors on psychometric measurements in ergonomics studies. A variety of sources can cause random measurement errors in ergonomics studies and these errors can distort virtually every statistic computed and lead investigators to erroneous conclusions. The effects of measurement errors on five most widely used statistical analysis tools have been discussed and illustrated: correlation; ANOVA; linear regression; factor analysis; linear discriminant analysis. It has been shown that measurement errors can greatly attenuate correlations between variables, reduce statistical power of ANOVA, distort (overestimate, underestimate or even change the sign of) regression coefficients, underrate the explanation contributions of the most important factors in factor analysis and depreciate the significance of discriminant function and discrimination abilities of individual variables in discrimination analysis. The discussions will be restricted to subjective scales and survey methods and their reliability estimates. Other methods applied in ergonomics research, such as physical and electrophysiological measurements and chemical and biomedical analysis methods, also have issues of measurement errors, but they are beyond the scope of this paper. As there has been increasing interest in the development and testing of theories in ergonomics research, it has become very important for ergonomics researchers to understand the effects of measurement errors on their experiment results, which the authors believe is very critical to research progress in theory development and cumulative knowledge in the ergonomics field.
Liu, Yingying; Sowmya, Arcot; Khamis, Heba
2018-01-01
Manually measured anthropometric quantities are used in many applications including human malnutrition assessment. Training is required to collect anthropometric measurements manually, which is not ideal in resource-constrained environments. Photogrammetric methods have been gaining attention in recent years, due to the availability and affordability of digital cameras. The primary goal is to demonstrate that height and mid-upper arm circumference (MUAC)-indicators of malnutrition-can be accurately estimated by applying linear regression to distance measurements from photographs of participants taken from five views, and determine the optimal view combinations. A secondary goal is to observe the effect on estimate error of two approaches which reduce complexity of the setup, computational requirements and the expertise required of the observer. Thirty-one participants (11 female, 20 male; 18-37 years) were photographed from five views. Distances were computed using both camera calibration and reference object techniques from manually annotated photos. To estimate height, linear regression was applied to the distances between the top of the participants head and the floor, as well as the height of a bounding box enclosing the participant's silhouette which eliminates the need to identify the floor. To estimate MUAC, linear regression was applied to the mid-upper arm width. Estimates were computed for all view combinations and performance was compared to other photogrammetric methods from the literature-linear distance method for height, and shape models for MUAC. The mean absolute difference (MAD) between the linear regression estimates and manual measurements were smaller compared to other methods. For the optimal view combinations (smallest MAD), the technical error of measurement and coefficient of reliability also indicate the linear regression methods are more reliable. The optimal view combination was the front and side views. When estimating height by linear
Error analysis of dimensionless scaling experiments with multiple points using linear regression
Guercan, Oe.D.; Vermare, L.; Hennequin, P.; Bourdelle, C.
2010-01-01
A general method of error estimation in the case of multiple point dimensionless scaling experiments, using linear regression and standard error propagation, is proposed. The method reduces to the previous result of Cordey (2009 Nucl. Fusion 49 052001) in the case of a two-point scan. On the other hand, if the points follow a linear trend, it explains how the estimated error decreases as more points are added to the scan. Based on the analytical expression that is derived, it is argued that for a low number of points, adding points to the ends of the scanned range, rather than the middle, results in a smaller error estimate. (letter)
Recovery coefficients as a test of system linearity of response in PET
Geworski, L.; Munz, D.L.; Knoop, B.; Hofmann, M.; Knapp, W.H.
2002-01-01
Aim: New imaging protocols have created an increasing demand for quantitation in dedicated PET. Besides attenuation and scatter correction the recovery correction, accounting for the instrument's limited spatial resolution, has gained importance. For clinical practicability these corrections should work independent from the object, i.e. from the actual distribution of emitter and absorber. Aim of the study was to test this object independency, i.e. system linearity of response, by comparing recovery coefficients (RC) determined for different object geometries. In fact, this comparison may serve as a final test on system linearity of response, as measured on the quantitative accuracy by which the activity concentration in small lesions can be recovered. Method: For hot and cold spot imaging situations spatial distribution of activity is different. Therefore, scatter correction algorithm has to deal with different scatter distributions. If all factors disturbing system linearity, specifically scatter and attenuation, are corrected to a sufficient degree of accuracy, the system behaves linearly resulting in the theoretical relationship. CSRC = (1-HSRC). Thus, this equation, applied hot and cold spot measurements, will serve as a test on the effectiveness of the corrections and, hence, as a test of system linearity of response. Following IEC standard procedures (IEC 61675-1) measurements were done with and without interplane septa (2D/3D) on an ECAT EXACT 922 using a cylindrical phantom containing six spheres of different diameters (10 mm - 40 mm). All data were corrected for attenuation (transmission scan) and scatter (2D: deconvolution, 3D: scatter model), as implemented in the scanner's standard software. Recovery coefficients were determined for cold (CSRC) and hot (HSRC) lesions using both 2D and 3D acquisition mode. Results: CSRC directly measured versus CSRC calculated according to eq. (1) from HSRC resulted in an excellent agreement for both 2D and 3D data
Dynamic Optimization for IPS2 Resource Allocation Based on Improved Fuzzy Multiple Linear Regression
Maokuan Zheng
2017-01-01
Full Text Available The study mainly focuses on resource allocation optimization for industrial product-service systems (IPS2. The development of IPS2 leads to sustainable economy by introducing cooperative mechanisms apart from commodity transaction. The randomness and fluctuation of service requests from customers lead to the volatility of IPS2 resource utilization ratio. Three basic rules for resource allocation optimization are put forward to improve system operation efficiency and cut unnecessary costs. An approach based on fuzzy multiple linear regression (FMLR is developed, which integrates the strength and concision of multiple linear regression in data fitting and factor analysis and the merit of fuzzy theory in dealing with uncertain or vague problems, which helps reduce those costs caused by unnecessary resource transfer. The iteration mechanism is introduced in the FMLR algorithm to improve forecasting accuracy. A case study of human resource allocation optimization in construction machinery industry is implemented to test and verify the proposed model.
COLOR IMAGE RETRIEVAL BASED ON FEATURE FUSION THROUGH MULTIPLE LINEAR REGRESSION ANALYSIS
K. Seetharaman
2015-08-01
Full Text Available This paper proposes a novel technique based on feature fusion using multiple linear regression analysis, and the least-square estimation method is employed to estimate the parameters. The given input query image is segmented into various regions according to the structure of the image. The color and texture features are extracted on each region of the query image, and the features are fused together using the multiple linear regression model. The estimated parameters of the model, which is modeled based on the features, are formed as a vector called a feature vector. The Canberra distance measure is adopted to compare the feature vectors of the query and target images. The F-measure is applied to evaluate the performance of the proposed technique. The obtained results expose that the proposed technique is comparable to the other existing techniques.
Lee, Eunjee; Zhu, Hongtu; Kong, Dehan; Wang, Yalin; Giovanello, Kelly Sullivan; Ibrahim, Joseph G
2015-12-01
The aim of this paper is to develop a Bayesian functional linear Cox regression model (BFLCRM) with both functional and scalar covariates. This new development is motivated by establishing the likelihood of conversion to Alzheimer's disease (AD) in 346 patients with mild cognitive impairment (MCI) enrolled in the Alzheimer's Disease Neuroimaging Initiative 1 (ADNI-1) and the early markers of conversion. These 346 MCI patients were followed over 48 months, with 161 MCI participants progressing to AD at 48 months. The functional linear Cox regression model was used to establish that functional covariates including hippocampus surface morphology and scalar covariates including brain MRI volumes, cognitive performance (ADAS-Cog), and APOE status can accurately predict time to onset of AD. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BFLCRM.
Inverse estimation of multiple muscle activations based on linear logistic regression.
Sekiya, Masashi; Tsuji, Toshiaki
2017-07-01
This study deals with a technology to estimate the muscle activity from the movement data using a statistical model. A linear regression (LR) model and artificial neural networks (ANN) have been known as statistical models for such use. Although ANN has a high estimation capability, it is often in the clinical application that the lack of data amount leads to performance deterioration. On the other hand, the LR model has a limitation in generalization performance. We therefore propose a muscle activity estimation method to improve the generalization performance through the use of linear logistic regression model. The proposed method was compared with the LR model and ANN in the verification experiment with 7 participants. As a result, the proposed method showed better generalization performance than the conventional methods in various tasks.
User's Guide to the Weighted-Multiple-Linear Regression Program (WREG version 1.0)
Eng, Ken; Chen, Yin-Yu; Kiang, Julie.E.
2009-01-01
Streamflow is not measured at every location in a stream network. Yet hydrologists, State and local agencies, and the general public still seek to know streamflow characteristics, such as mean annual flow or flood flows with different exceedance probabilities, at ungaged basins. The goals of this guide are to introduce and familiarize the user with the weighted multiple-linear regression (WREG) program, and to also provide the theoretical background for program features. The program is intended to be used to develop a regional estimation equation for streamflow characteristics that can be applied at an ungaged basin, or to improve the corresponding estimate at continuous-record streamflow gages with short records. The regional estimation equation results from a multiple-linear regression that relates the observable basin characteristics, such as drainage area, to streamflow characteristics.
Alzheimer's Disease Detection by Pseudo Zernike Moment and Linear Regression Classification.
Wang, Shui-Hua; Du, Sidan; Zhang, Yin; Phillips, Preetha; Wu, Le-Nan; Chen, Xian-Qing; Zhang, Yu-Dong
2017-01-01
This study presents an improved method based on "Gorji et al. Neuroscience. 2015" by introducing a relatively new classifier-linear regression classification. Our method selects one axial slice from 3D brain image, and employed pseudo Zernike moment with maximum order of 15 to extract 256 features from each image. Finally, linear regression classification was harnessed as the classifier. The proposed approach obtains an accuracy of 97.51%, a sensitivity of 96.71%, and a specificity of 97.73%. Our method performs better than Gorji's approach and five other state-of-the-art approaches. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.
On the Relationship Between Confidence Sets and Exchangeable Weights in Multiple Linear Regression.
Pek, Jolynn; Chalmers, R Philip; Monette, Georges
2016-01-01
When statistical models are employed to provide a parsimonious description of empirical relationships, the extent to which strong conclusions can be drawn rests on quantifying the uncertainty in parameter estimates. In multiple linear regression (MLR), regression weights carry two kinds of uncertainty represented by confidence sets (CSs) and exchangeable weights (EWs). Confidence sets quantify uncertainty in estimation whereas the set of EWs quantify uncertainty in the substantive interpretation of regression weights. As CSs and EWs share certain commonalities, we clarify the relationship between these two kinds of uncertainty about regression weights. We introduce a general framework describing how CSs and the set of EWs for regression weights are estimated from the likelihood-based and Wald-type approach, and establish the analytical relationship between CSs and sets of EWs. With empirical examples on posttraumatic growth of caregivers (Cadell et al., 2014; Schneider, Steele, Cadell & Hemsworth, 2011) and on graduate grade point average (Kuncel, Hezlett & Ones, 2001), we illustrate the usefulness of CSs and EWs for drawing strong scientific conclusions. We discuss the importance of considering both CSs and EWs as part of the scientific process, and provide an Online Appendix with R code for estimating Wald-type CSs and EWs for k regression weights.
MULTIPLE LINEAR REGRESSION ANALYSIS FOR PREDICTION OF BOILER LOSSES AND BOILER EFFICIENCY
Chayalakshmi C.L
2018-01-01
MULTIPLE LINEAR REGRESSION ANALYSIS FOR PREDICTION OF BOILER LOSSES AND BOILER EFFICIENCY ABSTRACT Calculation of boiler efficiency is essential if its parameters need to be controlled for either maintaining or enhancing its efficiency. But determination of boiler efficiency using conventional method is time consuming and very expensive. Hence, it is not recommended to find boiler efficiency frequently. The work presented in this paper deals with establishing the statistical mo...
Anderson, Carl A.; McRae, Allan F.; Visscher, Peter M.
2006-01-01
Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using...
The detection of influential subsets in linear regression using an influence matrix
Peña, Daniel; Yohai, Víctor J.
1991-01-01
This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentered covariance of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook's statistics in the diagonal. It is shown that points in an influential subset will appear with large weight in at least one of the eigenvector linked to the largest eigenvalue...
USE OF THE SIMPLE LINEAR REGRESSION MODEL IN MACRO-ECONOMICAL ANALYSES
Constantin ANGHELACHE
2011-10-01
Full Text Available The article presents the fundamental aspects of the linear regression, as a toolbox which can be used in macroeconomic analyses. The article describes the estimation of the parameters, the statistical tests used, the homoscesasticity and heteroskedasticity. The use of econometrics instrument in macroeconomics is an important factor that guarantees the quality of the models, analyses, results and possible interpretation that can be drawn at this level.
James W. Hardin; Henrik Schmeidiche; Raymond J. Carroll
2003-01-01
This paper discusses and illustrates the method of regression calibration. This is a straightforward technique for fitting models with additive measurement error. We present this discussion in terms of generalized linear models (GLMs) following the notation defined in Hardin and Carroll (2003). Discussion will include specified measurement error, measurement error estimated by replicate error-prone proxies, and measurement error estimated by instrumental variables. The discussion focuses on s...
Xu Li; Liang Changhong; Xiao Yuanqiu; Zhang Zhonglin
2010-01-01
Objective: To analyze the correlations between liver lipid level determined by liver 3.0 T 1 H-MRS in vivo and influencing factors using multiple linear stepwise regression. Methods: The prospective study of liver 1 H-MRS was performed with 3.0 T system and eight-channel torso phased-array coils using PRESS sequence. Forty-four volunteers were enrolled in this study. Liver spectra were collected with a TR of 1500 ms, TE of 30 ms, volume of interest of 2 cm×2 cm×2 cm, NSA of 64 times. The acquired raw proton MRS data were processed by using a software program SAGE. For each MRS measurement, using water as the internal reference, the amplitude of the lipid signal was normalized to the sum of the signal from lipid and water to obtain percentage lipid within the liver. The statistical description of height, weight, age and BMI, Line width and water suppression were recorded, and Pearson analysis was applied to test their relationships. Multiple linear stepwise regression was used to set the statistical model for the prediction of Liver lipid content. Results: Age (39.1±12.6) years, body weight (64.4±10.4) kg, BMI (23.3±3.1) kg/m 2 , linewidth (18.9±4.4) and the water suppression (90.7±6.5)% had significant correlation with liver lipid content (0.00 to 0.96%, median 0.02%), r were 0.11, 0.44, 0.40, 0.52, -0.73 respectively (P<0.05). But only age, BMI, line width, and the water suppression entered into the multiple linear regression equation. Liver lipid content prediction equation was as follows: Y= 1.395 - (0.021×water suppression) + (0.022×BMI) + (0.014×line width) - (0.004×age), and the coefficient of determination was 0. 613, corrected coefficient of determination was 0.59. Conclusion: The regression model fitted well, since the variables of age, BMI, width, and water suppression can explain about 60% of liver lipid content changes. (authors)
Ennouri, Karim; Ben Ayed, Rayda; Triki, Mohamed Ali; Ottaviani, Ennio; Mazzarello, Maura; Hertelli, Fathi; Zouari, Nabil
2017-07-01
The aim of the present work was to develop a model that supplies accurate predictions of the yields of delta-endotoxins and proteases produced by B. thuringiensis var. kurstaki HD-1. Using available medium ingredients as variables, a mathematical method, based on Plackett-Burman design (PB), was employed to analyze and compare data generated by the Bootstrap method and processed by multiple linear regressions (MLR) and artificial neural networks (ANN) including multilayer perceptron (MLP) and radial basis function (RBF) models. The predictive ability of these models was evaluated by comparison of output data through the determination of coefficient (R 2 ) and mean square error (MSE) values. The results demonstrate that the prediction of the yields of delta-endotoxin and protease was more accurate by ANN technique (87 and 89% for delta-endotoxin and protease determination coefficients, respectively) when compared with MLR method (73.1 and 77.2% for delta-endotoxin and protease determination coefficients, respectively), suggesting that the proposed ANNs, especially MLP, is a suitable new approach for determining yields of bacterial products that allow us to make more appropriate predictions in a shorter time and with less engineering effort.
Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.
Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo
2015-08-01
Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.
Privacy-Preserving Distributed Linear Regression on High-Dimensional Data
Gascón Adrià
2017-10-01
Full Text Available We propose privacy-preserving protocols for computing linear regression models, in the setting where the training dataset is vertically distributed among several parties. Our main contribution is a hybrid multi-party computation protocol that combines Yao’s garbled circuits with tailored protocols for computing inner products. Like many machine learning tasks, building a linear regression model involves solving a system of linear equations. We conduct a comprehensive evaluation and comparison of different techniques for securely performing this task, including a new Conjugate Gradient Descent (CGD algorithm. This algorithm is suitable for secure computation because it uses an efficient fixed-point representation of real numbers while maintaining accuracy and convergence rates comparable to what can be obtained with a classical solution using floating point numbers. Our technique improves on Nikolaenko et al.’s method for privacy-preserving ridge regression (S&P 2013, and can be used as a building block in other analyses. We implement a complete system and demonstrate that our approach is highly scalable, solving data analysis problems with one million records and one hundred features in less than one hour of total running time.
Apparent diffusion coefficient measurement in a moving phantom simulating linear respiratory motion.
Kwee, Thomas C; Takahara, Taro; Muro, Isao; Van Cauteren, Marc; Imai, Yutaka; Nievelstein, Rutger A J; Mali, Willem P T M; Luijten, Peter R
2010-10-01
The aim of this study was to examine the effect of simulated linear respiratory motion on apparent diffusion coefficient (ADC) measurements. Six rectangular test tubes (14 × 92 mm) filled with either water, tomato ketchup, or mayonnaise were positioned in a box containing agarose gel. This box was connected to a double-acting pneumatic cylinder, capable of inducing periodic linear motion in the long-axis direction of the magnetic bore (23-mm stroke). Diffusion-weighted magnetic resonance imaging was performed for both the static and moving phantoms, and ADC measurements were made in the six test tubes in both situations. In the three test tubes whose long axes were parallel to the direction of motion, ADCs agreed well between the moving and static phantom situations. However, in two test tubes that were filled with fluids that had a considerably lower diffusion coefficient than the surrounding agarose gel, and whose long axes were perpendicular to the direction of motion, the ADCs agreed poorly between the moving and static phantom situations. ADC measurements of large homogeneous structures are not affected by linear respiratory motion. However, ADC measurements of inhomogeneous or small structures are affected by linear respiratory motion due to partial volume effects.
Apparent diffusion coefficient measurement in a moving phantom simulating linear respiratory motion
Kwee, T.C.; Takahara, Taro; Nievelstein, R.A.J.; Mali, W.P.T.M.; Luijten, P.R.; Muro, Isao; Imai, Yutaka; Cauteren, M. Van
2010-01-01
The aim of this study was to examine the effect of simulated linear respiratory motion on apparent diffusion coefficient (ADC) measurements. Six rectangular test tubes (14 x 92 mm) filled with either water, tomato ketchup, or mayonnaise were positioned in a box containing agarose gel. This box was connected to a double-acting pneumatic cylinder, capable of inducing periodic linear motion in the long-axis direction of the magnetic bore (23-mm stroke). Diffusion-weighted magnetic resonance imaging was performed for both the static and moving phantoms, and ADC measurements were made in the six test tubes in both situations. In the three test tubes whose long axes were parallel to the direction of motion, ADCs agreed well between the moving and static phantom situations. However, in two test tubes that were filled with fluids that had a considerably lower diffusion coefficient than the surrounding agarose gel, and whose long axes were perpendicular to the direction of motion, the ADCs agreed poorly between the moving and static phantom situations. ADC measurements of large homogeneous structures are not affected by linear respiratory motion. However, ADC measurements of inhomogeneous or small structures are affected by linear respiratory motion due to partial volume effects. (author)
LINEAR REGRESSION MODEL ESTİMATİON FOR RIGHT CENSORED DATA
Ersin Yılmaz
2016-05-01
Full Text Available In this study, firstly we will define a right censored data. If we say shortly right-censored data is censoring values that above the exact line. This may be related with scaling device. And then we will use response variable acquainted from right-censored explanatory variables. Then the linear regression model will be estimated. For censored data’s existence, Kaplan-Meier weights will be used for the estimation of the model. With the weights regression model will be consistent and unbiased with that. And also there is a method for the censored data that is a semi parametric regression and this method also give useful results for censored data too. This study also might be useful for the health studies because of the censored data used in medical issues generally.
[Multiple linear regression analysis of X-ray measurement and WOMAC scores of knee osteoarthritis].
Ma, Yu-Feng; Wang, Qing-Fu; Chen, Zhao-Jun; Du, Chun-Lin; Li, Jun-Hai; Huang, Hu; Shi, Zong-Ting; Yin, Yue-Shan; Zhang, Lei; A-Di, Li-Jiang; Dong, Shi-Yu; Wu, Ji
2012-05-01
To perform Multiple Linear Regression analysis of X-ray measurement and WOMAC scores of knee osteoarthritis, and to analyze their relationship with clinical and biomechanical concepts. From March 2011 to July 2011, 140 patients (250 knees) were reviewed, including 132 knees in the left and 118 knees in the right; ranging in age from 40 to 71 years, with an average of 54.68 years. The MB-RULER measurement software was applied to measure femoral angle, tibial angle, femorotibial angle, joint gap angle from antero-posterir and lateral position of X-rays. The WOMAC scores were also collected. Then multiple regression equations was applied for the linear regression analysis of correlation between the X-ray measurement and WOMAC scores. There was statistical significance in the regression equation of AP X-rays value and WOMAC scores (Pregression equation of lateral X-ray value and WOMAC scores (P>0.05). 1) X-ray measurement of knee joint can reflect the WOMAC scores to a certain extent. 2) It is necessary to measure the X-ray mechanical axis of knee, which is important for diagnosis and treatment of osteoarthritis. 3) The correlation between tibial angle,joint gap angle on antero-posterior X-ray and WOMAC scores is significant, which can be used to assess the functional recovery of patients before and after treatment.
Using the fuzzy linear regression method to benchmark the energy efficiency of commercial buildings
Chung, William
2012-01-01
Highlights: ► Fuzzy linear regression method is used for developing benchmarking systems. ► The systems can be used to benchmark energy efficiency of commercial buildings. ► The resulting benchmarking model can be used by public users. ► The resulting benchmarking model can capture the fuzzy nature of input–output data. -- Abstract: Benchmarking systems from a sample of reference buildings need to be developed to conduct benchmarking processes for the energy efficiency of commercial buildings. However, not all benchmarking systems can be adopted by public users (i.e., other non-reference building owners) because of the different methods in developing such systems. An approach for benchmarking the energy efficiency of commercial buildings using statistical regression analysis to normalize other factors, such as management performance, was developed in a previous work. However, the field data given by experts can be regarded as a distribution of possibility. Thus, the previous work may not be adequate to handle such fuzzy input–output data. Consequently, a number of fuzzy structures cannot be fully captured by statistical regression analysis. This present paper proposes the use of fuzzy linear regression analysis to develop a benchmarking process, the resulting model of which can be used by public users. An illustrative example is given as well.
Madarang, Krish J; Kang, Joo-Hyon
2014-06-01
Stormwater runoff has been identified as a source of pollution for the environment, especially for receiving waters. In order to quantify and manage the impacts of stormwater runoff on the environment, predictive models and mathematical models have been developed. Predictive tools such as regression models have been widely used to predict stormwater discharge characteristics. Storm event characteristics, such as antecedent dry days (ADD), have been related to response variables, such as pollutant loads and concentrations. However it has been a controversial issue among many studies to consider ADD as an important variable in predicting stormwater discharge characteristics. In this study, we examined the accuracy of general linear regression models in predicting discharge characteristics of roadway runoff. A total of 17 storm events were monitored in two highway segments, located in Gwangju, Korea. Data from the monitoring were used to calibrate United States Environmental Protection Agency's Storm Water Management Model (SWMM). The calibrated SWMM was simulated for 55 storm events, and the results of total suspended solid (TSS) discharge loads and event mean concentrations (EMC) were extracted. From these data, linear regression models were developed. R(2) and p-values of the regression of ADD for both TSS loads and EMCs were investigated. Results showed that pollutant loads were better predicted than pollutant EMC in the multiple regression models. Regression may not provide the true effect of site-specific characteristics, due to uncertainty in the data. Copyright © 2014 The Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
Molnos, Sophie; Baumbach, Clemens; Wahl, Simone; Müller-Nurasyid, Martina; Strauch, Konstantin; Wang-Sattler, Rui; Waldenberger, Melanie; Meitinger, Thomas; Adamski, Jerzy; Kastenmüller, Gabi; Suhre, Karsten; Peters, Annette; Grallert, Harald; Theis, Fabian J; Gieger, Christian
2017-09-29
Genome-wide association studies allow us to understand the genetics of complex diseases. Human metabolism provides information about the disease-causing mechanisms, so it is usual to investigate the associations between genetic variants and metabolite levels. However, only considering genetic variants and their effects on one trait ignores the possible interplay between different "omics" layers. Existing tools only consider single-nucleotide polymorphism (SNP)-SNP interactions, and no practical tool is available for large-scale investigations of the interactions between pairs of arbitrary quantitative variables. We developed an R package called pulver to compute p-values for the interaction term in a very large number of linear regression models. Comparisons based on simulated data showed that pulver is much faster than the existing tools. This is achieved by using the correlation coefficient to test the null-hypothesis, which avoids the costly computation of inversions. Additional tricks are a rearrangement of the order, when iterating through the different "omics" layers, and implementing this algorithm in the fast programming language C++. Furthermore, we applied our algorithm to data from the German KORA study to investigate a real-world problem involving the interplay among DNA methylation, genetic variants, and metabolite levels. The pulver package is a convenient and rapid tool for screening huge numbers of linear regression models for significant interaction terms in arbitrary pairs of quantitative variables. pulver is written in R and C++, and can be downloaded freely from CRAN at https://cran.r-project.org/web/packages/pulver/ .
Verhelst, Helene E; Beele, Hilde; Joos, Rik; Vanneuville, Benedicte; Van Coster, Rudy N
2008-11-01
An 8-year-old girl with linear scleroderma "en coup de sabre" is reported who, at preschool age, presented with intractable simple partial seizures more than 1 year before skin lesions were first noticed. MRI revealed hippocampal atrophy, controlaterally to the seizures and ipsilaterally to the skin lesions. In the following months, a mental and motor regression was noticed. Cerebral CT scan showed multiple foci of calcifications in the affected hemisphere. In previously reported patients the skin lesions preceded the neurological signs. To the best of our knowledge, hippocampal atrophy was not earlier reported as presenting symptom of linear scleroderma. Linear scleroderma should be included in the differential diagnosis in patients with unilateral hippocampal atrophy even when the typical skin lesions are not present.
Yong, Yan Ling; Tan, Li Kuo; McLaughlin, Robert A.; Chee, Kok Han; Liew, Yih Miin
2017-12-01
Intravascular optical coherence tomography (OCT) is an optical imaging modality commonly used in the assessment of coronary artery diseases during percutaneous coronary intervention. Manual segmentation to assess luminal stenosis from OCT pullback scans is challenging and time consuming. We propose a linear-regression convolutional neural network to automatically perform vessel lumen segmentation, parameterized in terms of radial distances from the catheter centroid in polar space. Benchmarked against gold-standard manual segmentation, our proposed algorithm achieves average locational accuracy of the vessel wall of 22 microns, and 0.985 and 0.970 in Dice coefficient and Jaccard similarity index, respectively. The average absolute error of luminal area estimation is 1.38%. The processing rate is 40.6 ms per image, suggesting the potential to be incorporated into a clinical workflow and to provide quantitative assessment of vessel lumen in an intraoperative time frame.
Yong, Yan Ling; Tan, Li Kuo; McLaughlin, Robert A; Chee, Kok Han; Liew, Yih Miin
2017-12-01
Intravascular optical coherence tomography (OCT) is an optical imaging modality commonly used in the assessment of coronary artery diseases during percutaneous coronary intervention. Manual segmentation to assess luminal stenosis from OCT pullback scans is challenging and time consuming. We propose a linear-regression convolutional neural network to automatically perform vessel lumen segmentation, parameterized in terms of radial distances from the catheter centroid in polar space. Benchmarked against gold-standard manual segmentation, our proposed algorithm achieves average locational accuracy of the vessel wall of 22 microns, and 0.985 and 0.970 in Dice coefficient and Jaccard similarity index, respectively. The average absolute error of luminal area estimation is 1.38%. The processing rate is 40.6 ms per image, suggesting the potential to be incorporated into a clinical workflow and to provide quantitative assessment of vessel lumen in an intraoperative time frame. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).
Canto, Eduardo Leite do; Rittner, Roberto [Universidade Estadual de Campinas, SP (Brazil). Inst. de Quimica
1992-12-31
Calculation involving two variable linear regressions, require specific procedures generally not familiar to chemist. For attending the necessity of fast and efficient handling of NMR data, a self explained and Pc portable software has been developed, which allows user to produce and use diskette recorded tables, containing chemical shift or any other substituent physical-chemical measurements and constants ({sigma}{sub T}, {sigma}{sup o}{sub R}, E{sub s}, ...) 9 refs., 1 fig.
Improving the Prediction of Total Surgical Procedure Time Using Linear Regression Modeling.
Edelman, Eric R; van Kuijk, Sander M J; Hamaekers, Ankie E W; de Korte, Marcel J M; van Merode, Godefridus G; Buhre, Wolfgang F F A
2017-01-01
For efficient utilization of operating rooms (ORs), accurate schedules of assigned block time and sequences of patient cases need to be made. The quality of these planning tools is dependent on the accurate prediction of total procedure time (TPT) per case. In this paper, we attempt to improve the accuracy of TPT predictions by using linear regression models based on estimated surgeon-controlled time (eSCT) and other variables relevant to TPT. We extracted data from a Dutch benchmarking database of all surgeries performed in six academic hospitals in The Netherlands from 2012 till 2016. The final dataset consisted of 79,983 records, describing 199,772 h of total OR time. Potential predictors of TPT that were included in the subsequent analysis were eSCT, patient age, type of operation, American Society of Anesthesiologists (ASA) physical status classification, and type of anesthesia used. First, we computed the predicted TPT based on a previously described fixed ratio model for each record, multiplying eSCT by 1.33. This number is based on the research performed by van Veen-Berkx et al., which showed that 33% of SCT is generally a good approximation of anesthesia-controlled time (ACT). We then systematically tested all possible linear regression models to predict TPT using eSCT in combination with the other available independent variables. In addition, all regression models were again tested without eSCT as a predictor to predict ACT separately (which leads to TPT by adding SCT). TPT was most accurately predicted using a linear regression model based on the independent variables eSCT, type of operation, ASA classification, and type of anesthesia. This model performed significantly better than the fixed ratio model and the method of predicting ACT separately. Making use of these more accurate predictions in planning and sequencing algorithms may enable an increase in utilization of ORs, leading to significant financial and productivity related benefits.
Improving the Prediction of Total Surgical Procedure Time Using Linear Regression Modeling
Eric R. Edelman
2017-06-01
Full Text Available For efficient utilization of operating rooms (ORs, accurate schedules of assigned block time and sequences of patient cases need to be made. The quality of these planning tools is dependent on the accurate prediction of total procedure time (TPT per case. In this paper, we attempt to improve the accuracy of TPT predictions by using linear regression models based on estimated surgeon-controlled time (eSCT and other variables relevant to TPT. We extracted data from a Dutch benchmarking database of all surgeries performed in six academic hospitals in The Netherlands from 2012 till 2016. The final dataset consisted of 79,983 records, describing 199,772 h of total OR time. Potential predictors of TPT that were included in the subsequent analysis were eSCT, patient age, type of operation, American Society of Anesthesiologists (ASA physical status classification, and type of anesthesia used. First, we computed the predicted TPT based on a previously described fixed ratio model for each record, multiplying eSCT by 1.33. This number is based on the research performed by van Veen-Berkx et al., which showed that 33% of SCT is generally a good approximation of anesthesia-controlled time (ACT. We then systematically tested all possible linear regression models to predict TPT using eSCT in combination with the other available independent variables. In addition, all regression models were again tested without eSCT as a predictor to predict ACT separately (which leads to TPT by adding SCT. TPT was most accurately predicted using a linear regression model based on the independent variables eSCT, type of operation, ASA classification, and type of anesthesia. This model performed significantly better than the fixed ratio model and the method of predicting ACT separately. Making use of these more accurate predictions in planning and sequencing algorithms may enable an increase in utilization of ORs, leading to significant financial and productivity related
Caimmi, R.
2011-08-01
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both
Bruno, Delia Evelina; Barca, Emanuele; Goncalves, Rodrigo Mikosz; de Araujo Queiroz, Heithor Alexandre; Berardi, Luigi; Passarella, Giuseppe
2018-01-01
In this paper, the Evolutionary Polynomial Regression data modelling strategy has been applied to study small scale, short-term coastal morphodynamics, given its capability for treating a wide database of known information, non-linearly. Simple linear and multilinear regression models were also applied to achieve a balance between the computational load and reliability of estimations of the three models. In fact, even though it is easy to imagine that the more complex the model, the more the prediction improves, sometimes a "slight" worsening of estimations can be accepted in exchange for the time saved in data organization and computational load. The models' outcomes were validated through a detailed statistical, error analysis, which revealed a slightly better estimation of the polynomial model with respect to the multilinear model, as expected. On the other hand, even though the data organization was identical for the two models, the multilinear one required a simpler simulation setting and a faster run time. Finally, the most reliable evolutionary polynomial regression model was used in order to make some conjecture about the uncertainty increase with the extension of extrapolation time of the estimation. The overlapping rate between the confidence band of the mean of the known coast position and the prediction band of the estimated position can be a good index of the weakness in producing reliable estimations when the extrapolation time increases too much. The proposed models and tests have been applied to a coastal sector located nearby Torre Colimena in the Apulia region, south Italy.
Multiple regression technique for Pth degree polynominals with and without linear cross products
Davis, J. W.
1973-01-01
A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent analysis. To implement this technique, separate computer programs were developed for the case without linear cross products and for the case incorporating such cross products which evaluate the various constants in the model regression equation. In addition, the significance of the estimated regression equation is considered and the standard deviation, the F statistic, the maximum absolute percent error, and the average of the absolute values of the percent of error evaluated. The computer programs and their manner of utilization are described. Sample problems are included to illustrate the use and capability of the technique which show the output formats and typical plots comparing computer results to each set of input data.
Kiani, Alishir; Chwalibog, André; Nielsen, Mette O
2007-01-01
Late gestation energy expenditure (EE(gest)) originates from energy expenditure (EE) of development of conceptus (EE(conceptus)) and EE of homeorhetic adaptation of metabolism (EE(homeorhetic)). Even though EE(gest) is relatively easy to quantify, its partitioning is problematic. In the present...... study metabolizable energy (ME) intake ranges for twin-bearing ewes were 220-440, 350- 700, 350-900 kJ per metabolic body weight (W0.75) at week seven, five, two pre-partum respectively. Indirect calorimetry and a linear regression approach were used to quantify EE(gest) and then partition to EE......(conceptus) and EE(homeorhetic). Energy expenditure of basal metabolism of the non-gravid tissues (EE(bmng)), derived from the intercept of the linear regression equation of retained energy [kJ/W0.75] and ME intake [kJ/W(0.75)], was 298 [kJ/ W0.75]. Values of the intercepts of the regression equations at week seven...
Predicting recycling behaviour: Comparison of a linear regression model and a fuzzy logic model.
Vesely, Stepan; Klöckner, Christian A; Dohnal, Mirko
2016-03-01
In this paper we demonstrate that fuzzy logic can provide a better tool for predicting recycling behaviour than the customarily used linear regression. To show this, we take a set of empirical data on recycling behaviour (N=664), which we randomly divide into two halves. The first half is used to estimate a linear regression model of recycling behaviour, and to develop a fuzzy logic model of recycling behaviour. As the first comparison, the fit of both models to the data included in estimation of the models (N=332) is evaluated. As the second comparison, predictive accuracy of both models for "new" cases (hold-out data not included in building the models, N=332) is assessed. In both cases, the fuzzy logic model significantly outperforms the regression model in terms of fit. To conclude, when accurate predictions of recycling and possibly other environmental behaviours are needed, fuzzy logic modelling seems to be a promising technique. Copyright © 2015 Elsevier Ltd. All rights reserved.
Single Image Super-Resolution Using Global Regression Based on Multiple Local Linear Mappings.
Choi, Jae-Seok; Kim, Munchurl
2017-03-01
Super-resolution (SR) has become more vital, because of its capability to generate high-quality ultra-high definition (UHD) high-resolution (HR) images from low-resolution (LR) input images. Conventional SR methods entail high computational complexity, which makes them difficult to be implemented for up-scaling of full-high-definition input images into UHD-resolution images. Nevertheless, our previous super-interpolation (SI) method showed a good compromise between Peak-Signal-to-Noise Ratio (PSNR) performances and computational complexity. However, since SI only utilizes simple linear mappings, it may fail to precisely reconstruct HR patches with complex texture. In this paper, we present a novel SR method, which inherits the large-to-small patch conversion scheme from SI but uses global regression based on local linear mappings (GLM). Thus, our new SR method is called GLM-SI. In GLM-SI, each LR input patch is divided into 25 overlapped subpatches. Next, based on the local properties of these subpatches, 25 different local linear mappings are applied to the current LR input patch to generate 25 HR patch candidates, which are then regressed into one final HR patch using a global regressor. The local linear mappings are learned cluster-wise in our off-line training phase. The main contribution of this paper is as follows: Previously, linear-mapping-based conventional SR methods, including SI only used one simple yet coarse linear mapping to each patch to reconstruct its HR version. On the contrary, for each LR input patch, our GLM-SI is the first to apply a combination of multiple local linear mappings, where each local linear mapping is found according to local properties of the current LR patch. Therefore, it can better approximate nonlinear LR-to-HR mappings for HR patches with complex texture. Experiment results show that the proposed GLM-SI method outperforms most of the state-of-the-art methods, and shows comparable PSNR performance with much lower
Weighted functional linear regression models for gene-based association analysis.
Belonogova, Nadezhda M; Svishcheva, Gulnara R; Wilson, James F; Campbell, Harry; Axenovich, Tatiana I
2018-01-01
Functional linear regression models are effectively used in gene-based association analysis of complex traits. These models combine information about individual genetic variants, taking into account their positions and reducing the influence of noise and/or observation errors. To increase the power of methods, where several differently informative components are combined, weights are introduced to give the advantage to more informative components. Allele-specific weights have been introduced to collapsing and kernel-based approaches to gene-based association analysis. Here we have for the first time introduced weights to functional linear regression models adapted for both independent and family samples. Using data simulated on the basis of GAW17 genotypes and weights defined by allele frequencies via the beta distribution, we demonstrated that type I errors correspond to declared values and that increasing the weights of causal variants allows the power of functional linear models to be increased. We applied the new method to real data on blood pressure from the ORCADES sample. Five of the six known genes with P models. Moreover, we found an association between diastolic blood pressure and the VMP1 gene (P = 8.18×10-6), when we used a weighted functional model. For this gene, the unweighted functional and weighted kernel-based models had P = 0.004 and 0.006, respectively. The new method has been implemented in the program package FREGAT, which is freely available at https://cran.r-project.org/web/packages/FREGAT/index.html.
On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality
Olha P. Kupenko
2013-01-01
Full Text Available We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions.
Fast computation of the Maslov index for hyperbolic linear systems with periodic coefficients
Chardard, F; Dias, F; Bridges, T J
2006-01-01
The Maslov index is a topological property of periodic orbits of finite-dimensional Hamiltonian systems that is widely used in semiclassical quantization, quantum chaology, stability of waves and classical mechanics. The Maslov index is determined from the analysis of a linear Hamiltonian system with periodic coefficients. In this paper, a numerical scheme is devised to compute the Maslov index for hyperbolic linear systems when the phase space has a low dimension. The idea is to compute on the exterior algebra of the ambient vector space, where the Lagrangian subspace representing the unstable subspace is reduced to a line. When the exterior algebra is projectified the Lagrangian subspace always forms a closed loop. The idea is illustrated by application to Hamiltonian systems on a phase space of dimension 4. The theory is used to compute the Maslov index for the spectral problem associated with periodic solutions of the fifth-order Korteweg de Vries equation
Li, Hongjian; Leung, Kwong-Sak; Wong, Man-Hon; Ballester, Pedro J
2014-08-27
State-of-the-art protein-ligand docking methods are generally limited by the traditionally low accuracy of their scoring functions, which are used to predict binding affinity and thus vital for discriminating between active and inactive compounds. Despite intensive research over the years, classical scoring functions have reached a plateau in their predictive performance. These assume a predetermined additive functional form for some sophisticated numerical features, and use standard multivariate linear regression (MLR) on experimental data to derive the coefficients. In this study we show that such a simple functional form is detrimental for the prediction performance of a scoring function, and replacing linear regression by machine learning techniques like random forest (RF) can improve prediction performance. We investigate the conditions of applying RF under various contexts and find that given sufficient training samples RF manages to comprehensively capture the non-linearity between structural features and measured binding affinities. Incorporating more structural features and training with more samples can both boost RF performance. In addition, we analyze the importance of structural features to binding affinity prediction using the RF variable importance tool. Lastly, we use Cyscore, a top performing empirical scoring function, as a baseline for comparison study. Machine-learning scoring functions are fundamentally different from classical scoring functions because the former circumvents the fixed functional form relating structural features with binding affinities. RF, but not MLR, can effectively exploit more structural features and more training samples, leading to higher prediction performance. The future availability of more X-ray crystal structures will further widen the performance gap between RF-based and MLR-based scoring functions. This further stresses the importance of substituting RF for MLR in scoring function development.
Linear and support vector regressions based on geometrical correlation of data
Kaijun Wang
2007-10-01
Full Text Available Linear regression (LR and support vector regression (SVR are widely used in data analysis. Geometrical correlation learning (GcLearn was proposed recently to improve the predictive ability of LR and SVR through mining and using correlations between data of a variable (inner correlation. This paper theoretically analyzes prediction performance of the GcLearn method and proves that GcLearn LR and SVR will have better prediction performance than traditional LR and SVR for prediction tasks when good inner correlations are obtained and predictions by traditional LR and SVR are far away from their neighbor training data under inner correlation. This gives the applicable condition of GcLearn method.
Keilacker, H; Becker, G; Ziegler, M; Gottschling, H D [Zentralinstitut fuer Diabetes, Karlsburg (German Democratic Republic)
1980-10-01
In order to handle all types of radioimmunoassay (RIA) calibration curves obtained in the authors' laboratory in the same way, they tried to find a non-linear expression for their regression which allows calibration curves with different degrees of curvature to be fitted. Considering the two boundary cases of the incubation protocol they derived a hyperbolic inverse regression function: x = a/sub 1/y + a/sub 0/ + asub(-1)y/sup -1/, where x is the total concentration of antigen, asub(i) are constants, and y is the specifically bound radioactivity. An RIA evaluation procedure based on this function is described providing a fitted inverse RIA calibration curve and some statistical quality parameters. The latter are of an order which is normal for RIA systems. There is an excellent agreement between fitted and experimentally obtained calibration curves having a different degree of curvature.
Casero-Alonso, V; López-Fidalgo, J; Torsney, B
2017-01-01
Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space. MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [a, b] will be given for several standard weight functions. The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution. Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights. Copyright Â© 2016 Elsevier Ireland Ltd. All rights reserved.
Agarwal, Parul; Sambamoorthi, Usha
2015-12-01
Depression is common among individuals with osteoarthritis and leads to increased healthcare burden. The objective of this study was to examine excess total healthcare expenditures associated with depression among individuals with osteoarthritis in the US. Adults with self-reported osteoarthritis (n = 1881) were identified using data from the 2010 Medical Expenditure Panel Survey (MEPS). Among those with osteoarthritis, chi-square tests and ordinary least square regressions (OLS) were used to examine differences in healthcare expenditures between those with and without depression. Post-regression linear decomposition technique was used to estimate the relative contribution of different constructs of the Anderson's behavioral model, i.e., predisposing, enabling, need, personal healthcare practices, and external environment factors, to the excess expenditures associated with depression among individuals with osteoarthritis. All analysis accounted for the complex survey design of MEPS. Depression coexisted among 20.6 % of adults with osteoarthritis. The average total healthcare expenditures were $13,684 among adults with depression compared to $9284 among those without depression. Multivariable OLS regression revealed that adults with depression had 38.8 % higher healthcare expenditures (p regression linear decomposition analysis indicated that 50 % of differences in expenditures among adults with and without depression can be explained by differences in need factors. Among individuals with coexisting osteoarthritis and depression, excess healthcare expenditures associated with depression were mainly due to comorbid anxiety, chronic conditions and poor health status. These expenditures may potentially be reduced by providing timely intervention for need factors or by providing care under a collaborative care model.
Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data.
Ying, Gui-Shuang; Maguire, Maureen G; Glynn, Robert; Rosner, Bernard
2017-04-01
To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data. We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field in the elderly. When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI -0.03 to 0.32D, p = 0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, p = 0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller p-values, while analysis of the worse eye provided larger p-values than mixed effects models and marginal models. In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision.
Face Hallucination with Linear Regression Model in Semi-Orthogonal Multilinear PCA Method
Asavaskulkiet, Krissada
2018-04-01
In this paper, we propose a new face hallucination technique, face images reconstruction in HSV color space with a semi-orthogonal multilinear principal component analysis method. This novel hallucination technique can perform directly from tensors via tensor-to-vector projection by imposing the orthogonality constraint in only one mode. In our experiments, we use facial images from FERET database to test our hallucination approach which is demonstrated by extensive experiments with high-quality hallucinated color faces. The experimental results assure clearly demonstrated that we can generate photorealistic color face images by using the SO-MPCA subspace with a linear regression model.
Estimating integrated variance in the presence of microstructure noise using linear regression
Holý, Vladimír
2017-07-01
Using financial high-frequency data for estimation of integrated variance of asset prices is beneficial but with increasing number of observations so-called microstructure noise occurs. This noise can significantly bias the realized variance estimator. We propose a method for estimation of the integrated variance robust to microstructure noise as well as for testing the presence of the noise. Our method utilizes linear regression in which realized variances estimated from different data subsamples act as dependent variable while the number of observations act as explanatory variable. We compare proposed estimator with other methods on simulated data for several microstructure noise structures.
Avval Zhila Mohajeri
2015-01-01
Full Text Available This paper deals with developing a linear quantitative structure-activity relationship (QSAR model for predicting the RSK inhibition activity of some new compounds. A dataset consisting of 62 pyrazino [1,2-α] indole, diazepino [1,2-α] indole, and imidazole derivatives with known inhibitory activities was used. Multiple linear regressions (MLR technique combined with the stepwise (SW and the genetic algorithm (GA methods as variable selection tools was employed. For more checking stability, robustness and predictability of the proposed models, internal and external validation techniques were used. Comparison of the results obtained, indicate that the GA-MLR model is superior to the SW-MLR model and that it isapplicable for designing novel RSK inhibitors.
Linear attenuation coefficients of tissues from 1 keV to 150 keV
Böke, Aysun
2014-09-01
The linear attenuation coefficients and three interaction processes have been computed for liver, kidney, muscle, fat and for a range of x-ray energies from 1 keV to 150 keV. Molecular photoelectric absorption cross sections were calculated from atomic cross section data. Total coherent (Rayleigh) and incoherent (Compton) scattering cross sections were obtained by numerical integration over combinations of F2m(x) with the Thomson formula and Sm(x) with the Klein-Nishina formula, respectively. For the coherent (Rayleigh) scattering cross section calculations, molecular form factors were obtained from recent experimental data in the literature for values of xelements involved in tissue composition is 5 for liver, 47 for kidney, 44 for muscle and 3 for fat. The results are compared with previously published experimental and theoretical linear attenuation coefficients. In general, good agreement is obtained. The molecular form factors and scattering functions and cross sections are incorporated into a Monte Carlo program. The energy distributions of x-ray photons scattered from tissues have been simulated and the results are presented.
Estimating traffic volume on Wyoming low volume roads using linear and logistic regression methods
Dick Apronti
2016-12-01
Full Text Available Traffic volume is an important parameter in most transportation planning applications. Low volume roads make up about 69% of road miles in the United States. Estimating traffic on the low volume roads is a cost-effective alternative to taking traffic counts. This is because traditional traffic counts are expensive and impractical for low priority roads. The purpose of this paper is to present the development of two alternative means of cost-effectively estimating traffic volumes for low volume roads in Wyoming and to make recommendations for their implementation. The study methodology involves reviewing existing studies, identifying data sources, and carrying out the model development. The utility of the models developed were then verified by comparing actual traffic volumes to those predicted by the model. The study resulted in two regression models that are inexpensive and easy to implement. The first regression model was a linear regression model that utilized pavement type, access to highways, predominant land use types, and population to estimate traffic volume. In verifying the model, an R2 value of 0.64 and a root mean square error of 73.4% were obtained. The second model was a logistic regression model that identified the level of traffic on roads using five thresholds or levels. The logistic regression model was verified by estimating traffic volume thresholds and determining the percentage of roads that were accurately classified as belonging to the given thresholds. For the five thresholds, the percentage of roads classified correctly ranged from 79% to 88%. In conclusion, the verification of the models indicated both model types to be useful for accurate and cost-effective estimation of traffic volumes for low volume Wyoming roads. The models developed were recommended for use in traffic volume estimations for low volume roads in pavement management and environmental impact assessment studies.
Correlation coefficient based supervised locally linear embedding for pulmonary nodule recognition.
Wu, Panpan; Xia, Kewen; Yu, Hengyong
2016-11-01
Dimensionality reduction techniques are developed to suppress the negative effects of high dimensional feature space of lung CT images on classification performance in computer aided detection (CAD) systems for pulmonary nodule detection. An improved supervised locally linear embedding (SLLE) algorithm is proposed based on the concept of correlation coefficient. The Spearman's rank correlation coefficient is introduced to adjust the distance metric in the SLLE algorithm to ensure that more suitable neighborhood points could be identified, and thus to enhance the discriminating power of embedded data. The proposed Spearman's rank correlation coefficient based SLLE (SC(2)SLLE) is implemented and validated in our pilot CAD system using a clinical dataset collected from the publicly available lung image database consortium and image database resource initiative (LICD-IDRI). Particularly, a representative CAD system for solitary pulmonary nodule detection is designed and implemented. After a sequential medical image processing steps, 64 nodules and 140 non-nodules are extracted, and 34 representative features are calculated. The SC(2)SLLE, as well as SLLE and LLE algorithm, are applied to reduce the dimensionality. Several quantitative measurements are also used to evaluate and compare the performances. Using a 5-fold cross-validation methodology, the proposed algorithm achieves 87.65% accuracy, 79.23% sensitivity, 91.43% specificity, and 8.57% false positive rate, on average. Experimental results indicate that the proposed algorithm outperforms the original locally linear embedding and SLLE coupled with the support vector machine (SVM) classifier. Based on the preliminary results from a limited number of nodules in our dataset, this study demonstrates the great potential to improve the performance of a CAD system for nodule detection using the proposed SC(2)SLLE. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Elliott Campbell, J.; Moen, Jeremie C.; Ney, Richard A.; Schnoor, Jerald L.
2008-01-01
Estimates of forest soil organic carbon (SOC) have applications in carbon science, soil quality studies, carbon sequestration technologies, and carbon trading. Forest SOC has been modeled using a regression coefficient methodology that applies mean SOC densities (mass/area) to broad forest regions. A higher resolution model is based on an approach that employs a geographic information system (GIS) with soil databases and satellite-derived landcover images. Despite this advancement, the regression approach remains the basis of current state and federal level greenhouse gas inventories. Both approaches are analyzed in detail for Wisconsin forest soils from 1983 to 2001, applying rigorous error-fixing algorithms to soil databases. Resulting SOC stock estimates are 20% larger when determined using the GIS method rather than the regression approach. Average annual rates of increase in SOC stocks are 3.6 and 1.0 million metric tons of carbon per year for the GIS and regression approaches respectively. - Large differences in estimates of soil organic carbon stocks and annual changes in stocks for Wisconsin forestlands indicate a need for validation from forthcoming forest surveys
Lunt, Mark
2015-07-01
In the first article in this series we explored the use of linear regression to predict an outcome variable from a number of predictive factors. It assumed that the predictive factors were measured on an interval scale. However, this article shows how categorical variables can also be included in a linear regression model, enabling predictions to be made separately for different groups and allowing for testing the hypothesis that the outcome differs between groups. The use of interaction terms to measure whether the effect of a particular predictor variable differs between groups is also explained. An alternative approach to testing the difference between groups of the effect of a given predictor, which consists of measuring the effect in each group separately and seeing whether the statistical significance differs between the groups, is shown to be misleading. © The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
da Silva, Claudia Pereira; Emídio, Elissandro Soares; de Marchi, Mary Rosa Rodrigues
2015-01-01
This paper describes the validation of a method consisting of solid-phase extraction followed by gas chromatography-tandem mass spectrometry for the analysis of the ultraviolet (UV) filters benzophenone-3, ethylhexyl salicylate, ethylhexyl methoxycinnamate and octocrylene. The method validation criteria included evaluation of selectivity, analytical curve, trueness, precision, limits of detection and limits of quantification. The non-weighted linear regression model has traditionally been used for calibration, but it is not necessarily the optimal model in all cases. Because the assumption of homoscedasticity was not met for the analytical data in this work, a weighted least squares linear regression was used for the calibration method. The evaluated analytical parameters were satisfactory for the analytes and showed recoveries at four fortification levels between 62% and 107%, with relative standard deviations less than 14%. The detection limits ranged from 7.6 to 24.1 ng L(-1). The proposed method was used to determine the amount of UV filters in water samples from water treatment plants in Araraquara and Jau in São Paulo, Brazil. Copyright © 2014 Elsevier B.V. All rights reserved.
Grotti, Marco; Abelmoschi, Maria Luisa; Soggia, Francesco; Tiberiade, Christian; Frache, Roberto
2000-12-01
The multivariate effects of Na, K, Mg and Ca as nitrates on the electrothermal atomisation of manganese, cadmium and iron were studied by multiple linear regression modelling. Since the models proved to efficiently predict the effects of the considered matrix elements in a wide range of concentrations, they were applied to correct the interferences occurring in the determination of trace elements in seawater after pre-concentration of the analytes. In order to obtain a statistically significant number of samples, a large volume of the certified seawater reference materials CASS-3 and NASS-3 was treated with Chelex-100 resin; then, the chelating resin was separated from the solution, divided into several sub-samples, each of them was eluted with nitric acid and analysed by electrothermal atomic absorption spectrometry (for trace element determinations) and inductively coupled plasma optical emission spectrometry (for matrix element determinations). To minimise any other systematic error besides that due to matrix effects, accuracy of the pre-concentration step and contamination levels of the procedure were checked by inductively coupled plasma mass spectrometric measurements. Analytical results obtained by applying the multiple linear regression models were compared with those obtained with other calibration methods, such as external calibration using acid-based standards, external calibration using matrix-matched standards and the analyte addition technique. Empirical models proved to efficiently reduce interferences occurring in the analysis of real samples, allowing an improvement of accuracy better than for other calibration methods.
A Feature-Free 30-Disease Pathological Brain Detection System by Linear Regression Classifier.
Chen, Yi; Shao, Ying; Yan, Jie; Yuan, Ti-Fei; Qu, Yanwen; Lee, Elizabeth; Wang, Shuihua
2017-01-01
Alzheimer's disease patients are increasing rapidly every year. Scholars tend to use computer vision methods to develop automatic diagnosis system. (Background) In 2015, Gorji et al. proposed a novel method using pseudo Zernike moment. They tested four classifiers: learning vector quantization neural network, pattern recognition neural network trained by Levenberg-Marquardt, by resilient backpropagation, and by scaled conjugate gradient. This study presents an improved method by introducing a relatively new classifier-linear regression classification. Our method selects one axial slice from 3D brain image, and employed pseudo Zernike moment with maximum order of 15 to extract 256 features from each image. Finally, linear regression classification was harnessed as the classifier. The proposed approach obtains an accuracy of 97.51%, a sensitivity of 96.71%, and a specificity of 97.73%. Our method performs better than Gorji's approach and five other state-of-the-art approaches. Therefore, it can be used to detect Alzheimer's disease. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.
Rafiei, Hamid; Khanzadeh, Marziyeh; Mozaffari, Shahla; Bostanifar, Mohammad Hassan; Avval, Zhila Mohajeri; Aalizadeh, Reza; Pourbasheer, Eslam
2016-01-01
Quantitative structure-activity relationship (QSAR) study has been employed for predicting the inhibitory activities of the Hepatitis C virus (HCV) NS5B polymerase inhibitors . A data set consisted of 72 compounds was selected, and then different types of molecular descriptors were calculated. The whole data set was split into a training set (80 % of the dataset) and a test set (20 % of the dataset) using principle component analysis. The stepwise (SW) and the genetic algorithm (GA) techniques were used as variable selection tools. Multiple linear regression method was then used to linearly correlate the selected descriptors with inhibitory activities. Several validation technique including leave-one-out and leave-group-out cross-validation, Y-randomization method were used to evaluate the internal capability of the derived models. The external prediction ability of the derived models was further analyzed using modified r(2), concordance correlation coefficient values and Golbraikh and Tropsha acceptable model criteria's. Based on the derived results (GA-MLR), some new insights toward molecular structural requirements for obtaining better inhibitory activity were obtained.
Misyura, Maksym; Sukhai, Mahadeo A; Kulasignam, Vathany; Zhang, Tong; Kamel-Reid, Suzanne; Stockley, Tracy L
2018-02-01
A standard approach in test evaluation is to compare results of the assay in validation to results from previously validated methods. For quantitative molecular diagnostic assays, comparison of test values is often performed using simple linear regression and the coefficient of determination (R 2 ), using R 2 as the primary metric of assay agreement. However, the use of R 2 alone does not adequately quantify constant or proportional errors required for optimal test evaluation. More extensive statistical approaches, such as Bland-Altman and expanded interpretation of linear regression methods, can be used to more thoroughly compare data from quantitative molecular assays. We present the application of Bland-Altman and linear regression statistical methods to evaluate quantitative outputs from next-generation sequencing assays (NGS). NGS-derived data sets from assay validation experiments were used to demonstrate the utility of the statistical methods. Both Bland-Altman and linear regression were able to detect the presence and magnitude of constant and proportional error in quantitative values of NGS data. Deming linear regression was used in the context of assay comparison studies, while simple linear regression was used to analyse serial dilution data. Bland-Altman statistical approach was also adapted to quantify assay accuracy, including constant and proportional errors, and precision where theoretical and empirical values were known. The complementary application of the statistical methods described in this manuscript enables more extensive evaluation of performance characteristics of quantitative molecular assays, prior to implementation in the clinical molecular laboratory. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
EP-based wavelet coefficient quantization for linear distortion ECG data compression.
Hung, King-Chu; Wu, Tsung-Ching; Lee, Hsieh-Wei; Liu, Tung-Kuan
2014-07-01
Reconstruction quality maintenance is of the essence for ECG data compression due to the desire for diagnosis use. Quantization schemes with non-linear distortion characteristics usually result in time-consuming quality control that blocks real-time application. In this paper, a new wavelet coefficient quantization scheme based on an evolution program (EP) is proposed for wavelet-based ECG data compression. The EP search can create a stationary relationship among the quantization scales of multi-resolution levels. The stationary property implies that multi-level quantization scales can be controlled with a single variable. This hypothesis can lead to a simple design of linear distortion control with 3-D curve fitting technology. In addition, a competitive strategy is applied for alleviating data dependency effect. By using the ECG signals saved in MIT and PTB databases, many experiments were undertaken for the evaluation of compression performance, quality control efficiency, data dependency influence. The experimental results show that the new EP-based quantization scheme can obtain high compression performance and keep linear distortion behavior efficiency. This characteristic guarantees fast quality control even for the prediction model mismatching practical distortion curve. Copyright © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
Effect of Different Concrete Grade on Radiation Linear Attenuation Coefficient (μ)
Noor Azreen Masenwat; Mohammad Shahrizan Samsu; Mohamad Pauzi Ismail; Suhairy Sani; Ismail Mustapha; Nasharuddin Isa; Mohamad Haniza Mahmud
2014-01-01
In calculating the quantity of absorption of radiation and its relationship with the thickness of a material, linear attenuation coefficient (μ) of the material is one of the parameters to be taken into account. For normal concrete, the (μ) varies depending on the type of radiation used, 0.105 cm -1 for Co-60 and 0.123 cm -1 for Cs-137. Value (μ) is used in the calculation of the radiation absorption for concrete material does not take into account factors such concrete grades. In this research, concrete with different grades (Grade 15, Grade 20, Grade 25, Grade 30, Grade 35, Grade 40) are designed and manufactured with reference to the mixing method described in British Standard. Then, the linear attenuation (μ) for each grade are measured using the radiation from the source Co-60 and Cs-137 sources. This paper describes and discusses the impact of differences in concrete grade of linear attenuation (μ) for Co-60 source/ source Cs-137 and its relationship with the compressive strength. (author)
Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models.
Wiedermann, Wolfgang; Artner, Richard; von Eye, Alexander
2017-01-01
Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.
Weichenthal, Scott; Ryswyk, Keith Van; Goldstein, Alon; Bagg, Scott; Shekkarizfard, Maryam; Hatzopoulou, Marianne
2016-04-01
Existing evidence suggests that ambient ultrafine particles (UFPs) (regression model for UFPs in Montreal, Canada using mobile monitoring data collected from 414 road segments during the summer and winter months between 2011 and 2012. Two different approaches were examined for model development including standard multivariable linear regression and a machine learning approach (kernel-based regularized least squares (KRLS)) that learns the functional form of covariate impacts on ambient UFP concentrations from the data. The final models included parameters for population density, ambient temperature and wind speed, land use parameters (park space and open space), length of local roads and rail, and estimated annual average NOx emissions from traffic. The final multivariable linear regression model explained 62% of the spatial variation in ambient UFP concentrations whereas the KRLS model explained 79% of the variance. The KRLS model performed slightly better than the linear regression model when evaluated using an external dataset (R(2)=0.58 vs. 0.55) or a cross-validation procedure (R(2)=0.67 vs. 0.60). In general, our findings suggest that the KRLS approach may offer modest improvements in predictive performance compared to standard multivariable linear regression models used to estimate spatial variations in ambient UFPs. However, differences in predictive performance were not statistically significant when evaluated using the cross-validation procedure. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.
Camporesi, Roberto
2016-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.
More, Anand Govind; Gupta, Sunil Kumar
2018-03-24
Bioelectrochemical system (BES) is a novel, self-sustaining metal removal technology functioning on the utilization of chemical energy of organic matter with the help of microorganisms. Experimental trials of two chambered BES reactor were conducted with varying substrate concentration using sodium acetate (500 mg/L to 2000 mg/L COD) and different initial chromium concentration (Cr i ) (10-100 mg/L) at different cathode pH (pH 1-7). In the current study mathematical models based on multiple linear regression (MLR) and non-linear regression (NLR) approach were developed using laboratory experimental data for determining chromium removal efficiency (CRE) in the cathode chamber of BES. Substrate concentration, rate of substrate consumption, Cr i , pH, temperature and hydraulic retention time (HRT) were the operating process parameters of the reactor considered for development of the proposed models. MLR showed a better correlation coefficient (0.972) as compared to NLR (0.952). Validation of the models using t-test analysis revealed unbiasedness of both the models, with t critical value (2.04) greater than t-calculated values for MLR (-0.708) and NLR (-0.86). The root-mean-square error (RMSE) for MLR and NLR were 5.06 % and 7.45 %, respectively. Comparison between both models suggested MLR to be best suited model for predicting the chromium removal behavior using the BES technology to specify a set of operating conditions for BES. Modelling the behavior of CRE will be helpful for scale up of BES technology at industrial level. Copyright © 2018 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.
Dawson, Terence P.; Curran, Paul J.; Kupiec, John A.
1995-01-01
link between wavelengths chosen by stepwise regression and the biochemical of interest, and this in turn has cast doubts on the use of imaging spectrometry for the estimation of foliar biochemical concentrations at sites distant from the training sites. To investigate this problem, an analysis was conducted on the variation in canopy biochemical concentrations and reflectance spectra using forced entry linear regression.
Deconinck, E; Zhang, M H; Petitet, F; Dubus, E; Ijjaali, I; Coomans, D; Vander Heyden, Y
2008-02-18
The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.
Da Silva Pinto, P.S.; Eustache, R.P.; Audenaert, M.; Bernassau, J.M.
1996-01-01
This work deals with carbon 13 nuclear magnetic resonance chemical shifts empiric calculations by multi linear regression and molecular modeling. The multi linear regression is indeed one way to obtain an equation able to describe the behaviour of the chemical shift for some molecules which are in the data base (rigid molecules with carbons). The methodology consists of structures describer parameters definition which can be bound to carbon 13 chemical shift known for these molecules. Then, the linear regression is used to determine the equation significant parameters. This one can be extrapolated to molecules which presents some resemblances with those of the data base. (O.L.). 20 refs., 4 figs., 1 tab
Thermal Coefficient of Linear Expansion Modified by Dendritic Segregation in Nickel-Iron Alloys
Ogorodnikova, O. M.; Maksimova, E. V.
2018-05-01
The paper presents investigations of thermal properties of Fe-Ni and Fe-Ni-Co casting alloys affected by the heterogeneous distribution of their chemical elements. It is shown that nickel dendritic segregation has a negative effect on properties of studied invars. A mathematical model is proposed to explore the influence of nickel dendritic segregation on the thermal coefficient of linear expansion (TCLE) of the alloy. A computer simulation of TCLE of Fe-Ni-Co superinvars is performed with regard to a heterogeneous distribution of their chemical elements over the whole volume. The ProLigSol computer software application is developed for processing the data array and results of computer simulation.
Region specific optimization of continuous linear attenuation coefficients based on UTE (RESOLUTE)
Ladefoged, Claes N; Benoit, Didier; Law, Ian
2015-01-01
The reconstruction of PET brain data in a PET/MR hybrid scanner is challenging in the absence of transmission sources, where MR images are used for MR-based attenuation correction (MR-AC). The main challenge of MR-AC is to separate bone and air, as neither have a signal in traditional MR images......-valued linear attenuation coefficients in bone that provides accurate reconstructed PET image data. A total of 164 [(18)F]FDG PET/MR patients were included in this study, of which 10 were used for training. MR-AC was based on either standard CT (reference), UTE or our method (RESOLUTE). The reconstructed PET...... on the reconstructed PET images, as well as limiting the number and extent of the outliers....
Yu Shao-De; Wu Shi-Bin; Xie Yao-Qin; Wang Hao-Yu; Wei Xin-Hua; Chen Xin; Pan Wan-Long; Hu Jiani
2015-01-01
Similarity coefficient mapping (SCM) aims to improve the morphological evaluation of weighted magnetic resonance imaging However, how to interpret the generated SCM map is still pending. Moreover, is it probable to extract tissue dissimilarity messages based on the theory behind SCM? The primary purpose of this paper is to address these two questions. First, the theory of SCM was interpreted from the perspective of linear fitting. Then, a term was embedded for tissue dissimilarity information. Finally, our method was validated with sixteen human brain image series from multi-echo . Generated maps were investigated from signal-to-noise ratio (SNR) and perceived visual quality, and then interpreted from intra- and inter-tissue intensity. Experimental results show that both perceptibility of anatomical structures and tissue contrast are improved. More importantly, tissue similarity or dissimilarity can be quantified and cross-validated from pixel intensity analysis. This method benefits image enhancement, tissue classification, malformation detection and morphological evaluation. (paper)
Hariharan, M; Chee, Lim Sin; Yaacob, Sazali
2012-06-01
Acoustic analysis of infant cry signals has been proven to be an excellent tool in the area of automatic detection of pathological status of an infant. This paper investigates the application of parameter weighting for linear prediction cepstral coefficients (LPCCs) to provide the robust representation of infant cry signals. Three classes of infant cry signals were considered such as normal cry signals, cry signals from deaf babies and babies with asphyxia. A Probabilistic Neural Network (PNN) is suggested to classify the infant cry signals into normal and pathological cries. PNN is trained with different spread factor or smoothing parameter to obtain better classification accuracy. The experimental results demonstrate that the suggested features and classification algorithms give very promising classification accuracy of above 98% and it expounds that the suggested method can be used to help medical professionals for diagnosing pathological status of an infant from cry signals.
Słania J.
2014-10-01
Full Text Available The article presents the process of production of coated electrodes and their welding properties. The factors concerning the welding properties and the currently applied method of assessing are given. The methodology of the testing based on the measuring and recording of instantaneous values of welding current and welding arc voltage is discussed. Algorithm for creation of reference data base of the expert system is shown, aiding the assessment of covered electrodes welding properties. The stability of voltage–current characteristics was discussed. Statistical factors of instantaneous values of welding current and welding arc voltage waveforms used for determining of welding process stability are presented. The results of coated electrodes welding properties are compared. The article presents the results of linear regression as well as the impact of the independent variables on the welding process performance. Finally the conclusions drawn from the research are given.
Dlugosz, Stephan; Mammen, Enno; Wilke, Ralf
2017-01-01
Large data sets that originate from administrative or operational activity are increasingly used for statistical analysis as they often contain very precise information and a large number of observations. But there is evidence that some variables can be subject to severe misclassification...... or contain missing values. Given the size of the data, a flexible semiparametric misclassification model would be good choice but their use in practise is scarce. To close this gap a semiparametric model for the probability of observing labour market transitions is estimated using a sample of 20 m...... observations from Germany. It is shown that estimated marginal effects of a number of covariates are sizeably affected by misclassification and missing values in the analysis data. The proposed generalized partially linear regression extends existing models by allowing a misclassified discrete covariate...
hMuLab: A Biomedical Hybrid MUlti-LABel Classifier Based on Multiple Linear Regression.
Wang, Pu; Ge, Ruiquan; Xiao, Xuan; Zhou, Manli; Zhou, Fengfeng
2017-01-01
Many biomedical classification problems are multi-label by nature, e.g., a gene involved in a variety of functions and a patient with multiple diseases. The majority of existing classification algorithms assumes each sample with only one class label, and the multi-label classification problem remains to be a challenge for biomedical researchers. This study proposes a novel multi-label learning algorithm, hMuLab, by integrating both feature-based and neighbor-based similarity scores. The multiple linear regression modeling techniques make hMuLab capable of producing multiple label assignments for a query sample. The comparison results over six commonly-used multi-label performance measurements suggest that hMuLab performs accurately and stably for the biomedical datasets, and may serve as a complement to the existing literature.
Linear regression models and k-means clustering for statistical analysis of fNIRS data.
Bonomini, Viola; Zucchelli, Lucia; Re, Rebecca; Ieva, Francesca; Spinelli, Lorenzo; Contini, Davide; Paganoni, Anna; Torricelli, Alessandro
2015-02-01
We propose a new algorithm, based on a linear regression model, to statistically estimate the hemodynamic activations in fNIRS data sets. The main concern guiding the algorithm development was the minimization of assumptions and approximations made on the data set for the application of statistical tests. Further, we propose a K-means method to cluster fNIRS data (i.e. channels) as activated or not activated. The methods were validated both on simulated and in vivo fNIRS data. A time domain (TD) fNIRS technique was preferred because of its high performances in discriminating cortical activation and superficial physiological changes. However, the proposed method is also applicable to continuous wave or frequency domain fNIRS data sets.
Multiple Linear Regression Model Based on Neural Network and Its Application in the MBR Simulation
Chunqing Li
2012-01-01
Full Text Available The computer simulation of the membrane bioreactor MBR has become the research focus of the MBR simulation. In order to compensate for the defects, for example, long test period, high cost, invisible equipment seal, and so forth, on the basis of conducting in-depth study of the mathematical model of the MBR, combining with neural network theory, this paper proposed a three-dimensional simulation system for MBR wastewater treatment, with fast speed, high efficiency, and good visualization. The system is researched and developed with the hybrid programming of VC++ programming language and OpenGL, with a multifactor linear regression model of affecting MBR membrane fluxes based on neural network, applying modeling method of integer instead of float and quad tree recursion. The experiments show that the three-dimensional simulation system, using the above models and methods, has the inspiration and reference for the future research and application of the MBR simulation technology.
Chen, Wen-Yuan; Wang, Mei; Fu, Zhou-Xing
2014-01-01
Most railway accidents happen at railway crossings. Therefore, how to detect humans or objects present in the risk area of a railway crossing and thus prevent accidents are important tasks. In this paper, three strategies are used to detect the risk area of a railway crossing: (1) we use a terrain drop compensation (TDC) technique to solve the problem of the concavity of railway crossings; (2) we use a linear regression technique to predict the position and length of an object from image processing; (3) we have developed a novel strategy called calculating local maximum Y-coordinate object points (CLMYOP) to obtain the ground points of the object. In addition, image preprocessing is also applied to filter out the noise and successfully improve the object detection. From the experimental results, it is demonstrated that our scheme is an effective and corrective method for the detection of railway crossing risk areas. PMID:24936948
Wen-Yuan Chen
2014-06-01
Full Text Available Most railway accidents happen at railway crossings. Therefore, how to detect humans or objects present in the risk area of a railway crossing and thus prevent accidents are important tasks. In this paper, three strategies are used to detect the risk area of a railway crossing: (1 we use a terrain drop compensation (TDC technique to solve the problem of the concavity of railway crossings; (2 we use a linear regression technique to predict the position and length of an object from image processing; (3 we have developed a novel strategy called calculating local maximum Y-coordinate object points (CLMYOP to obtain the ground points of the object. In addition, image preprocessing is also applied to filter out the noise and successfully improve the object detection. From the experimental results, it is demonstrated that our scheme is an effective and corrective method for the detection of railway crossing risk areas.
Rodríguez-Barranco, Miguel; Tobías, Aurelio; Redondo, Daniel; Molina-Portillo, Elena; Sánchez, María José
2017-03-17
Meta-analysis is very useful to summarize the effect of a treatment or a risk factor for a given disease. Often studies report results based on log-transformed variables in order to achieve the principal assumptions of a linear regression model. If this is the case for some, but not all studies, the effects need to be homogenized. We derived a set of formulae to transform absolute changes into relative ones, and vice versa, to allow including all results in a meta-analysis. We applied our procedure to all possible combinations of log-transformed independent or dependent variables. We also evaluated it in a simulation based on two variables either normally or asymmetrically distributed. In all the scenarios, and based on different change criteria, the effect size estimated by the derived set of formulae was equivalent to the real effect size. To avoid biased estimates of the effect, this procedure should be used with caution in the case of independent variables with asymmetric distributions that significantly differ from the normal distribution. We illustrate an application of this procedure by an application to a meta-analysis on the potential effects on neurodevelopment in children exposed to arsenic and manganese. The procedure proposed has been shown to be valid and capable of expressing the effect size of a linear regression model based on different change criteria in the variables. Homogenizing the results from different studies beforehand allows them to be combined in a meta-analysis, independently of whether the transformations had been performed on the dependent and/or independent variables.
Yoo, Yun Joo; Sun, Lei; Poirier, Julia G; Paterson, Andrew D; Bull, Shelley B
2017-02-01
By jointly analyzing multiple variants within a gene, instead of one at a time, gene-based multiple regression can improve power, robustness, and interpretation in genetic association analysis. We investigate multiple linear combination (MLC) test statistics for analysis of common variants under realistic trait models with linkage disequilibrium (LD) based on HapMap Asian haplotypes. MLC is a directional test that exploits LD structure in a gene to construct clusters of closely correlated variants recoded such that the majority of pairwise correlations are positive. It combines variant effects within the same cluster linearly, and aggregates cluster-specific effects in a quadratic sum of squares and cross-products, producing a test statistic with reduced degrees of freedom (df) equal to the number of clusters. By simulation studies of 1000 genes from across the genome, we demonstrate that MLC is a well-powered and robust choice among existing methods across a broad range of gene structures. Compared to minimum P-value, variance-component, and principal-component methods, the mean power of MLC is never much lower than that of other methods, and can be higher, particularly with multiple causal variants. Moreover, the variation in gene-specific MLC test size and power across 1000 genes is less than that of other methods, suggesting it is a complementary approach for discovery in genome-wide analysis. The cluster construction of the MLC test statistics helps reveal within-gene LD structure, allowing interpretation of clustered variants as haplotypic effects, while multiple regression helps to distinguish direct and indirect associations. © 2016 The Authors Genetic Epidemiology Published by Wiley Periodicals, Inc.
Rico Rico, A.; Droge, S.T.J.|info:eu-repo/dai/nl/304834017; Hermens, J.L.M.|info:eu-repo/dai/nl/069681384
2010-01-01
The effect of the molecular structure and the salinity on the sorption of the anionic surfactant linear alkylbenzenesulfonate (LAS) to marine sediment has been studied. The analysis of several individual LAS congeners in seawater and of one specific LAS congener at different dilutions of seawater
Shuke, Noriyuki
1991-01-01
In hepatobiliary scintigraphy, kinetic model analysis, which provides kinetic parameters like hepatic extraction or excretion rate, have been done for quantitative evaluation of liver function. In this analysis, unknown model parameters are usually determined using nonlinear least square regression method (NLS method) where iterative calculation and initial estimate for unknown parameters are required. As a simple alternative to NLS method, direct integral linear least square regression method (DILS method), which can determine model parameters by a simple calculation without initial estimate, is proposed, and tested the applicability to analysis of hepatobiliary scintigraphy. In order to see whether DILS method could determine model parameters as good as NLS method, or to determine appropriate weight for DILS method, simulated theoretical data based on prefixed parameters were fitted to 1 compartment model using both DILS method with various weightings and NLS method. The parameter values obtained were then compared with prefixed values which were used for data generation. The effect of various weights on the error of parameter estimate was examined, and inverse of time was found to be the best weight to make the error minimum. When using this weight, DILS method could give parameter values close to those obtained by NLS method and both parameter values were very close to prefixed values. With appropriate weighting, the DILS method could provide reliable parameter estimate which is relatively insensitive to the data noise. In conclusion, the DILS method could be used as a simple alternative to NLS method, providing reliable parameter estimate. (author)
Neck-focused panic attacks among Cambodian refugees; a logistic and linear regression analysis.
Hinton, Devon E; Chhean, Dara; Pich, Vuth; Um, Khin; Fama, Jeanne M; Pollack, Mark H
2006-01-01
Consecutive Cambodian refugees attending a psychiatric clinic were assessed for the presence and severity of current--i.e., at least one episode in the last month--neck-focused panic. Among the whole sample (N=130), in a logistic regression analysis, the Anxiety Sensitivity Index (ASI; odds ratio=3.70) and the Clinician-Administered PTSD Scale (CAPS; odds ratio=2.61) significantly predicted the presence of current neck panic (NP). Among the neck panic patients (N=60), in the linear regression analysis, NP severity was significantly predicted by NP-associated flashbacks (beta=.42), NP-associated catastrophic cognitions (beta=.22), and CAPS score (beta=.28). Further analysis revealed the effect of the CAPS score to be significantly mediated (Sobel test [Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182]) by both NP-associated flashbacks and catastrophic cognitions. In the care of traumatized Cambodian refugees, NP severity, as well as NP-associated flashbacks and catastrophic cognitions, should be specifically assessed and treated.
Adi Syahputra
2014-03-01
Full Text Available Quantitative structure activity relationship (QSAR for 21 insecticides of phthalamides containing hydrazone (PCH was studied using multiple linear regression (MLR, principle component regression (PCR and artificial neural network (ANN. Five descriptors were included in the model for MLR and ANN analysis, and five latent variables obtained from principle component analysis (PCA were used in PCR analysis. Calculation of descriptors was performed using semi-empirical PM6 method. ANN analysis was found to be superior statistical technique compared to the other methods and gave a good correlation between descriptors and activity (r2 = 0.84. Based on the obtained model, we have successfully designed some new insecticides with higher predicted activity than those of previously synthesized compounds, e.g.2-(decalinecarbamoyl-5-chloro-N’-((5-methylthiophen-2-ylmethylene benzohydrazide, 2-(decalinecarbamoyl-5-chloro-N’-((thiophen-2-yl-methylene benzohydrazide and 2-(decaline carbamoyl-N’-(4-fluorobenzylidene-5-chlorobenzohydrazide with predicted log LC50 of 1.640, 1.672, and 1.769 respectively.
Rubio, Francisco J.
2016-02-09
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry. We propose a general noninformative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions. We extend these propriety results to cases where the response variables are censored. The latter scenario is of interest in the context of accelerated failure time models, which are relevant in survival analysis. We present a simulation study that demonstrates good frequentist properties of the posterior credible intervals associated with the proposed priors. This study also sheds some light on the trade-off between increased model flexibility and the risk of over-fitting. We illustrate the performance of the proposed models with real data. Although we focus on models with univariate response variables, we also present some extensions to the multivariate case in the Supporting Information.
Fernández-Fernández, Mario; Rodríguez-González, Pablo; García Alonso, J Ignacio
2016-10-01
We have developed a novel, rapid and easy calculation procedure for Mass Isotopomer Distribution Analysis based on multiple linear regression which allows the simultaneous calculation of the precursor pool enrichment and the fraction of newly synthesized labelled proteins (fractional synthesis) using linear algebra. To test this approach, we used the peptide RGGGLK as a model tryptic peptide containing three subunits of glycine. We selected glycine labelled in two 13 C atoms ( 13 C 2 -glycine) as labelled amino acid to demonstrate that spectral overlap is not a problem in the proposed methodology. The developed methodology was tested first in vitro by changing the precursor pool enrichment from 10 to 40% of 13 C 2 -glycine. Secondly, a simulated in vivo synthesis of proteins was designed by combining the natural abundance RGGGLK peptide and 10 or 20% 13 C 2 -glycine at 1 : 1, 1 : 3 and 3 : 1 ratios. Precursor pool enrichments and fractional synthesis values were calculated with satisfactory precision and accuracy using a simple spreadsheet. This novel approach can provide a relatively rapid and easy means to measure protein turnover based on stable isotope tracers. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Association of footprint measurements with plantar kinetics: a linear regression model.
Fascione, Jeanna M; Crews, Ryan T; Wrobel, James S
2014-03-01
The use of foot measurements to classify morphology and interpret foot function remains one of the focal concepts of lower-extremity biomechanics. However, only 27% to 55% of midfoot variance in foot pressures has been determined in the most comprehensive models. We investigated whether dynamic walking footprint measurements are associated with inter-individual foot loading variability. Thirty individuals (15 men and 15 women; mean ± SD age, 27.17 ± 2.21 years) walked at a self-selected speed over an electronic pedography platform using the midgait technique. Kinetic variables (contact time, peak pressure, pressure-time integral, and force-time integral) were collected for six masked regions. Footprints were digitized for area and linear boundaries using digital photo planimetry software. Six footprint measurements were determined: contact area, footprint index, arch index, truncated arch index, Chippaux-Smirak index, and Staheli index. Linear regression analysis with a Bonferroni adjustment was performed to determine the association between the footprint measurements and each of the kinetic variables. The findings demonstrate that a relationship exists between increased midfoot contact and increased kinetic values in respective locations. Many of these variables produced large effect sizes while describing 38% to 71% of the common variance of select plantar kinetic variables in the medial midfoot region. In addition, larger footprints were associated with larger kinetic values at the medial heel region and both masked forefoot regions. Dynamic footprint measurements are associated with dynamic plantar loading kinetics, with emphasis on the midfoot region.
Kwan, Johnny S H; Kung, Annie W C; Sham, Pak C
2011-09-01
Selective genotyping can increase power in quantitative trait association. One example of selective genotyping is two-tail extreme selection, but simple linear regression analysis gives a biased genetic effect estimate. Here, we present a simple correction for the bias.
Camporesi, Roberto
2016-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…
A. D. Pataraya
1997-01-01
Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.
Zounemat-Kermani, Mohammad
2012-08-01
In this study, the ability of two models of multi linear regression (MLR) and Levenberg-Marquardt (LM) feed-forward neural network was examined to estimate the hourly dew point temperature. Dew point temperature is the temperature at which water vapor in the air condenses into liquid. This temperature can be useful in estimating meteorological variables such as fog, rain, snow, dew, and evapotranspiration and in investigating agronomical issues as stomatal closure in plants. The availability of hourly records of climatic data (air temperature, relative humidity and pressure) which could be used to predict dew point temperature initiated the practice of modeling. Additionally, the wind vector (wind speed magnitude and direction) and conceptual input of weather condition were employed as other input variables. The three quantitative standard statistical performance evaluation measures, i.e. the root mean squared error, mean absolute error, and absolute logarithmic Nash-Sutcliffe efficiency coefficient ( {| {{{Log}}({{NS}})} |} ) were employed to evaluate the performances of the developed models. The results showed that applying wind vector and weather condition as input vectors along with meteorological variables could slightly increase the ANN and MLR predictive accuracy. The results also revealed that LM-NN was superior to MLR model and the best performance was obtained by considering all potential input variables in terms of different evaluation criteria.
Wang, D Z; Wang, C; Shen, C F; Zhang, Y; Zhang, H; Song, G D; Xue, X D; Xu, Z L; Zhang, S; Jiang, G H
2017-05-10
We described the time trend of acute myocardial infarction (AMI) from 1999 to 2013 in Tianjin incidence rate with Cochran-Armitage trend (CAT) test and linear regression analysis, and the results were compared. Based on actual population, CAT test had much stronger statistical power than linear regression analysis for both overall incidence trend and age specific incidence trend (Cochran-Armitage trend P valuelinear regression P value). The statistical power of CAT test decreased, while the result of linear regression analysis remained the same when population size was reduced by 100 times and AMI incidence rate remained unchanged. The two statistical methods have their advantages and disadvantages. It is necessary to choose statistical method according the fitting degree of data, or comprehensively analyze the results of two methods.
A new modified conjugate gradient coefficient for solving system of linear equations
Hajar, N.; ‘Aini, N.; Shapiee, N.; Abidin, Z. Z.; Khadijah, W.; Rivaie, M.; Mamat, M.
2017-09-01
Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations
Development of statistical linear regression model for metals from transportation land uses.
Maniquiz, Marla C; Lee, Soyoung; Lee, Eunju; Kim, Lee-Hyung
2009-01-01
The transportation landuses possessing impervious surfaces such as highways, parking lots, roads, and bridges were recognized as the highly polluted non-point sources (NPSs) in the urban areas. Lots of pollutants from urban transportation are accumulating on the paved surfaces during dry periods and are washed-off during a storm. In Korea, the identification and monitoring of NPSs still represent a great challenge. Since 2004, the Ministry of Environment (MOE) has been engaged in several researches and monitoring to develop stormwater management policies and treatment systems for future implementation. The data over 131 storm events during May 2004 to September 2008 at eleven sites were analyzed to identify correlation relationships between particulates and metals, and to develop simple linear regression (SLR) model to estimate event mean concentration (EMC). Results indicate that there was no significant relationship between metals and TSS EMC. However, the SLR estimation models although not providing useful results are valuable indicators of high uncertainties that NPS pollution possess. Therefore, long term monitoring employing proper methods and precise statistical analysis of the data should be undertaken to eliminate these uncertainties.
Claudia Ledesma
2013-08-01
Full Text Available Water quality is traditionally monitored and evaluated based upon field data collected at limited locations. The storage capacity of reservoirs is reduced by deposits of suspended matter. The major factors affecting surface water quality are suspended sediments, chlorophyll and nutrients. Modeling and monitoring the biogeochemical status of reservoirs can be done through data from remote sensors. Since the improvement of sensors’ spatial and spectral resolutions, satellites have been used to monitor the interior areas of bodies of water. Water quality parameters, such as chlorophyll-a concentration and secchi disk depth, were found to have a high correlation with transformed spectral variables derived from bands 1, 2, 3 and 4 of LANDSAT 5TM satellite. We created models of estimated responses in regard to values of chlorophyll-a. To do so, we used population models of single and multiple linear regression, whose parameters are associated with the reflectance data of bands 2 and 4 of the sub-image of the satellite, as well as the data of chlorophyll-a obtained in 25 selected stations. According to the physico-chemical analyzes performed, the characteristics of the water in the reservoir of Rio Tercero, correspond to somewhat hard freshwater with calcium bicarbonate. The water was classified as usable as a source of plant treatment, excellent for irrigation because of its low salinity and low residual sodium carbonate content, but unsuitable for animal consumption because of its low salt content.
An Application of Robust Method in Multiple Linear Regression Model toward Credit Card Debt
Amira Azmi, Nur; Saifullah Rusiman, Mohd; Khalid, Kamil; Roslan, Rozaini; Sufahani, Suliadi; Mohamad, Mahathir; Salleh, Rohayu Mohd; Hamzah, Nur Shamsidah Amir
2018-04-01
Credit card is a convenient alternative replaced cash or cheque, and it is essential component for electronic and internet commerce. In this study, the researchers attempt to determine the relationship and significance variables between credit card debt and demographic variables such as age, household income, education level, years with current employer, years at current address, debt to income ratio and other debt. The provided data covers 850 customers information. There are three methods that applied to the credit card debt data which are multiple linear regression (MLR) models, MLR models with least quartile difference (LQD) method and MLR models with mean absolute deviation method. After comparing among three methods, it is found that MLR model with LQD method became the best model with the lowest value of mean square error (MSE). According to the final model, it shows that the years with current employer, years at current address, household income in thousands and debt to income ratio are positively associated with the amount of credit debt. Meanwhile variables for age, level of education and other debt are negatively associated with amount of credit debt. This study may serve as a reference for the bank company by using robust methods, so that they could better understand their options and choice that is best aligned with their goals for inference regarding to the credit card debt.
C. Makendran
2015-01-01
Full Text Available Prediction models for low volume village roads in India are developed to evaluate the progression of different types of distress such as roughness, cracking, and potholes. Even though the Government of India is investing huge quantum of money on road construction every year, poor control over the quality of road construction and its subsequent maintenance is leading to the faster road deterioration. In this regard, it is essential that scientific maintenance procedures are to be evolved on the basis of performance of low volume flexible pavements. Considering the above, an attempt has been made in this research endeavor to develop prediction models to understand the progression of roughness, cracking, and potholes in flexible pavements exposed to least or nil routine maintenance. Distress data were collected from the low volume rural roads covering about 173 stretches spread across Tamil Nadu state in India. Based on the above collected data, distress prediction models have been developed using multiple linear regression analysis. Further, the models have been validated using independent field data. It can be concluded that the models developed in this study can serve as useful tools for the practicing engineers maintaining flexible pavements on low volume roads.
Liu, Ke; Chen, Xiaojing; Li, Limin; Chen, Huiling; Ruan, Xiukai; Liu, Wenbin
2015-02-09
The successive projections algorithm (SPA) is widely used to select variables for multiple linear regression (MLR) modeling. However, SPA used only once may not obtain all the useful information of the full spectra, because the number of selected variables cannot exceed the number of calibration samples in the SPA algorithm. Therefore, the SPA-MLR method risks the loss of useful information. To make a full use of the useful information in the spectra, a new method named "consensus SPA-MLR" (C-SPA-MLR) is proposed herein. This method is the combination of consensus strategy and SPA-MLR method. In the C-SPA-MLR method, SPA-MLR is used to construct member models with different subsets of variables, which are selected from the remaining variables iteratively. A consensus prediction is obtained by combining the predictions of the member models. The proposed method is evaluated by analyzing the near infrared (NIR) spectra of corn and diesel. The results of C-SPA-MLR method showed a better prediction performance compared with the SPA-MLR and full-spectra PLS methods. Moreover, these results could serve as a reference for combination the consensus strategy and other variable selection methods when analyzing NIR spectra and other spectroscopic techniques. Copyright © 2014 Elsevier B.V. All rights reserved.
Zhang, Xiaodong; Zhao, Yinxia; Hu, Shaoyong; Hao, Shuai; Yan, Jiewen; Zhang, Lingyan; Zhao, Jing; Li, Shaolin
2015-09-01
To investigate the correlation between the lumbar vertebra bone mineral density (BMD) and age, gender, height, weight, body mass index, waistline, hipline, bone marrow and abdomen fat, and to explore the key factor affecting the BMD. A total of 72 cases were randomly recruited. All the subjects underwent a spectroscopic examination of the third lumber vertebra with single-voxel method in 1.5T MR. Lipid fractions (FF%) were measured. Quantitative CT were also performed to get the BMD of L3 and the corresponding abdomen subcutaneous adipose tissue (SAT) and visceral adipose tissue (VAT). The statistical analysis were performed by SPSS 19.0. Multiple linear regression showed except the age and FF% showed significant difference (P0.05). The correlation of age and FF% with BMD was statistically negatively significant (r=-0.830, -0.521, P<0.05). The ROC curve analysis showed that the sensitivety and specificity of predicting osteoporosis were 81.8% and 86.9%, with a threshold of 58.5 years old. And it showed that the sensitivety and specificity of predicting osteoporosis were 90.9% and 55.7%, with a threshold of 52.8% for FF%. The lumbar vertebra BMD was significantly and negatively correlated with age and bone marrow FF%, but it was not significantly correlated with gender, height, weight, BMI, waistline, hipline, SAT and VAT. And age was the critical factor.
Non-linear auto-regressive models for cross-frequency coupling in neural time series
Tallot, Lucille; Grabot, Laetitia; Doyère, Valérie; Grenier, Yves; Gramfort, Alexandre
2017-01-01
We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling. PMID:29227989
Shayan, Zahra; Mohammad Gholi Mezerji, Naser; Shayan, Leila; Naseri, Parisa
2015-11-03
Logistic regression (LR) and linear discriminant analysis (LDA) are two popular statistical models for prediction of group membership. Although they are very similar, the LDA makes more assumptions about the data. When categorical and continuous variables used simultaneously, the optimal choice between the two models is questionable. In most studies, classification error (CE) is used to discriminate between subjects in several groups, but this index is not suitable to predict the accuracy of the outcome. The present study compared LR and LDA models using classification indices. This cross-sectional study selected 243 cancer patients. Sample sets of different sizes (n = 50, 100, 150, 200, 220) were randomly selected and the CE, B, and Q classification indices were calculated by the LR and LDA models. CE revealed the a lack of superiority for one model over the other, but the results showed that LR performed better than LDA for the B and Q indices in all situations. No significant effect for sample size on CE was noted for selection of an optimal model. Assessment of the accuracy of prediction of real data indicated that the B and Q indices are appropriate for selection of an optimal model. The results of this study showed that LR performs better in some cases and LDA in others when based on CE. The CE index is not appropriate for classification, although the B and Q indices performed better and offered more efficient criteria for comparison and discrimination between groups.
An Ionospheric Index Model based on Linear Regression and Neural Network Approaches
Tshisaphungo, Mpho; McKinnell, Lee-Anne; Bosco Habarulema, John
2017-04-01
The ionosphere is well known to reflect radio wave signals in the high frequency (HF) band due to the present of electron and ions within the region. To optimise the use of long distance HF communications, it is important to understand the drivers of ionospheric storms and accurately predict the propagation conditions especially during disturbed days. This paper presents the development of an ionospheric storm-time index over the South African region for the application of HF communication users. The model will result into a valuable tool to measure the complex ionospheric behaviour in an operational space weather monitoring and forecasting environment. The development of an ionospheric storm-time index is based on a single ionosonde station data over Grahamstown (33.3°S,26.5°E), South Africa. Critical frequency of the F2 layer (foF2) measurements for a period 1996-2014 were considered for this study. The model was developed based on linear regression and neural network approaches. In this talk validation results for low, medium and high solar activity periods will be discussed to demonstrate model's performance.
Mumtaz, Ubaidullah; Ali, Yousaf; Petrillo, Antonella
2018-05-15
The increase in the environmental pollution is one of the most important topic in today's world. In this context, the industrial activities can pose a significant threat to the environment. To manage problems associate to industrial activities several methods, techniques and approaches have been developed. Green supply chain management (GSCM) is considered one of the most important "environmental management approach". In developing countries such as Pakistan the implementation of GSCM practices is still in its initial stages. Lack of knowledge about its effects on economic performance is the reason because of industries fear to implement these practices. The aim of this research is to perceive the effects of GSCM practices on organizational performance in Pakistan. In this research the GSCM practices considered are: internal practices, external practices, investment recovery and eco-design. While, the performance parameters considered are: environmental pollution, operational cost and organizational flexibility. A set of hypothesis propose the effect of each GSCM practice on the performance parameters. Factor analysis and linear regression are used to analyze the survey data of Pakistani industries, in order to authenticate these hypotheses. The findings of this research indicate a decrease in environmental pollution and operational cost with the implementation of GSCM practices, whereas organizational flexibility has not improved for Pakistani industries. These results aim to help managers regarding their decision of implementing GSCM practices in the industrial sector of Pakistan. Copyright © 2017 Elsevier B.V. All rights reserved.
Zhan, Xinhua; Liang, Xiao; Xu, Guohua; Zhou, Lixiang
2013-01-01
Polycyclic aromatic hydrocarbons (PAHs) are contaminants that reside mainly in surface soils. Dietary intake of plant-based foods can make a major contribution to total PAH exposure. Little information is available on the relationship between root morphology and plant uptake of PAHs. An understanding of plant root morphologic and compositional factors that affect root uptake of contaminants is important and can inform both agricultural (chemical contamination of crops) and engineering (phytoremediation) applications. Five crop plant species are grown hydroponically in solutions containing the PAH phenanthrene. Measurements are taken for 1) phenanthrene uptake, 2) root morphology – specific surface area, volume, surface area, tip number and total root length and 3) root tissue composition – water, lipid, protein and carbohydrate content. These factors are compared through Pearson's correlation and multiple linear regression analysis. The major factors which promote phenanthrene uptake are specific surface area and lipid content. -- Highlights: •There is no correlation between phenanthrene uptake and total root length, and water. •Specific surface area and lipid are the most crucial factors for phenanthrene uptake. •The contribution of specific surface area is greater than that of lipid. -- The contribution of specific surface area is greater than that of lipid in the two most important root morphological and compositional factors affecting phenanthrene uptake
Forecasting on the total volumes of Malaysia's imports and exports by multiple linear regression
Beh, W. L.; Yong, M. K. Au
2017-04-01
This study is to give an insight on the doubt of the important of macroeconomic variables that affecting the total volumes of Malaysia's imports and exports by using multiple linear regression (MLR) analysis. The time frame for this study will be determined by using quarterly data of the total volumes of Malaysia's imports and exports covering the period between 2000-2015. The macroeconomic variables will be limited to eleven variables which are the exchange rate of US Dollar with Malaysia Ringgit (USD-MYR), exchange rate of China Yuan with Malaysia Ringgit (RMB-MYR), exchange rate of European Euro with Malaysia Ringgit (EUR-MYR), exchange rate of Singapore Dollar with Malaysia Ringgit (SGD-MYR), crude oil prices, gold prices, producer price index (PPI), interest rate, consumer price index (CPI), industrial production index (IPI) and gross domestic product (GDP). This study has applied the Johansen Co-integration test to investigate the relationship among the total volumes to Malaysia's imports and exports. The result shows that crude oil prices, RMB-MYR, EUR-MYR and IPI play important roles in the total volumes of Malaysia's imports. Meanwhile crude oil price, USD-MYR and GDP play important roles in the total volumes of Malaysia's exports.
Bunyamin, Muhammad Afif; Yap, Keem Siah; Aziz, Nur Liyana Afiqah Abdul; Tiong, Sheih Kiong; Wong, Shen Yuong; Kamal, Md Fauzan
2013-01-01
This paper presents a new approach of gas emission estimation in power generation plant using a hybrid Genetic Algorithm (GA) and Linear Regression (LR) (denoted as GA-LR). The LR is one of the approaches that model the relationship between an output dependant variable, y, with one or more explanatory variables or inputs which denoted as x. It is able to estimate unknown model parameters from inputs data. On the other hand, GA is used to search for the optimal solution until specific criteria is met causing termination. These results include providing good solutions as compared to one optimal solution for complex problems. Thus, GA is widely used as feature selection. By combining the LR and GA (GA-LR), this new technique is able to select the most important input features as well as giving more accurate prediction by minimizing the prediction errors. This new technique is able to produce more consistent of gas emission estimation, which may help in reducing population to the environment. In this paper, the study's interest is focused on nitrous oxides (NOx) prediction. The results of the experiment are encouraging.
Correction of TRMM 3B42V7 Based on Linear Regression Models over China
Shaohua Liu
2016-01-01
Full Text Available High temporal-spatial precipitation is necessary for hydrological simulation and water resource management, and remotely sensed precipitation products (RSPPs play a key role in supporting high temporal-spatial precipitation, especially in sparse gauge regions. TRMM 3B42V7 data (TRMM precipitation is an essential RSPP outperforming other RSPPs. Yet the utilization of TRMM precipitation is still limited by the inaccuracy and low spatial resolution at regional scale. In this paper, linear regression models (LRMs have been constructed to correct and downscale the TRMM precipitation based on the gauge precipitation at 2257 stations over China from 1998 to 2013. Then, the corrected TRMM precipitation was validated by gauge precipitation at 839 out of 2257 stations in 2014 at station and grid scales. The results show that both monthly and annual LRMs have obviously improved the accuracy of corrected TRMM precipitation with acceptable error, and monthly LRM performs slightly better than annual LRM in Mideastern China. Although the performance of corrected TRMM precipitation from the LRMs has been increased in Northwest China and Tibetan plateau, the error of corrected TRMM precipitation is still significant due to the large deviation between TRMM precipitation and low-density gauge precipitation.
Linear electro-optic coefficient in multilayer self-organized InAs quantum dot structures
Akca, I.B.; Dana, A.; Aydinli, A.; Rossetti, M.; Li, L.; Dagli, N.; Fiore, A.
2007-01-01
The electro-optic coefficients of self-organized InAs quantum dot layers in molecular beam epitaxy grown laser structures in reverse bias have been investigated. Enhanced electrooptic coefficients compared to bulk GaAs were observed.
Mehmet Das
2018-01-01
Full Text Available In this study, an air heated solar collector (AHSC dryer was designed to determine the drying characteristics of the pear. Flat pear slices of 10 mm thickness were used in the experiments. The pears were dried both in the AHSC dryer and under the sun. Panel glass temperature, panel floor temperature, panel inlet temperature, panel outlet temperature, drying cabinet inlet temperature, drying cabinet outlet temperature, drying cabinet temperature, drying cabinet moisture, solar radiation, pear internal temperature, air velocity and mass loss of pear were measured at 30 min intervals. Experiments were carried out during the periods of June 2017 in Elazig, Turkey. The experiments started at 8:00 a.m. and continued till 18:00. The experiments were continued until the weight changes in the pear slices stopped. Wet basis moisture content (MCw, dry basis moisture content (MCd, adjustable moisture ratio (MR, drying rate (DR, and convective heat transfer coefficient (hc were calculated with both in the AHSC dryer and the open sun drying experiment data. It was found that the values of hc in both drying systems with a range 12.4 and 20.8 W/m2 °C. Three different kernel models were used in the support vector machine (SVM regression to construct the predictive model of the calculated hc values for both systems. The mean absolute error (MAE, root mean squared error (RMSE, relative absolute error (RAE and root relative absolute error (RRAE analysis were performed to indicate the predictive model’s accuracy. As a result, the rate of drying of the pear was examined for both systems and it was observed that the pear had dried earlier in the AHSC drying system. A predictive model was obtained using the SVM regression for the calculated hc values for the pear in the AHSC drying system. The normalized polynomial kernel was determined as the best kernel model in SVM for estimating the hc values.
Faridah Hani Mohamed Salleh
2017-01-01
Full Text Available Gene regulatory network (GRN reconstruction is the process of identifying regulatory gene interactions from experimental data through computational analysis. One of the main reasons for the reduced performance of previous GRN methods had been inaccurate prediction of cascade motifs. Cascade error is defined as the wrong prediction of cascade motifs, where an indirect interaction is misinterpreted as a direct interaction. Despite the active research on various GRN prediction methods, the discussion on specific methods to solve problems related to cascade errors is still lacking. In fact, the experiments conducted by the past studies were not specifically geared towards proving the ability of GRN prediction methods in avoiding the occurrences of cascade errors. Hence, this research aims to propose Multiple Linear Regression (MLR to infer GRN from gene expression data and to avoid wrongly inferring of an indirect interaction (A → B → C as a direct interaction (A → C. Since the number of observations of the real experiment datasets was far less than the number of predictors, some predictors were eliminated by extracting the random subnetworks from global interaction networks via an established extraction method. In addition, the experiment was extended to assess the effectiveness of MLR in dealing with cascade error by using a novel experimental procedure that had been proposed in this work. The experiment revealed that the number of cascade errors had been very minimal. Apart from that, the Belsley collinearity test proved that multicollinearity did affect the datasets used in this experiment greatly. All the tested subnetworks obtained satisfactory results, with AUROC values above 0.5.
Herminiati, A.; Rahman, T.; Turmala, E.; Fitriany, C. G.
2017-12-01
The purpose of this study was to determine the correlation of different concentrations of modified cassava flour that was processed for banana fritter flour. The research method consists of two stages: (1) to determine the different types of flour: cassava flour, modified cassava flour-A (using the method of the lactid acid bacteria), and modified cassava flour-B (using the method of the autoclaving cooling cycle), then conducted on organoleptic test and physicochemical analysis; (2) to determine the correlation of concentration of modified cassava flour for banana fritter flour, by design was used simple linear regression. The factors were used different concentrations of modified cassava flour-B (y1) 40%, (y2) 50%, and (y3) 60%. The response in the study includes physical analysis (whiteness of flour, water holding capacity-WHC, oil holding capacity-OHC), chemical analysis (moisture content, ash content, crude fiber content, starch content), and organoleptic (color, aroma, taste, texture). The results showed that the type of flour selected from the organoleptic test was modified cassava flour-B. Analysis results of modified cassava flour-B component containing whiteness of flour 60.42%; WHC 41.17%; OHC 21.15%; moisture content 4.4%; ash content 1.75%; crude fiber content 1.86%; starch content 67.31%. The different concentrations of modified cassava flour-B with the results of the analysis provides correlation to the whiteness of flour, WHC, OHC, moisture content, ash content, crude fiber content, and starch content. The different concentrations of modified cassava flour-B does not affect the color, aroma, taste, and texture.
Wang, J; Wang, F; Liu, Y; Xu, J; Lin, H; Jia, B; Zuo, W; Jiang, Y; Hu, L; Lin, F
2016-01-01
Overweight individuals are at higher risk for developing type II diabetes than the general population. We conducted this study to analyze the correlation between blood glucose and biochemical parameters, and developed a blood glucose prediction model tailored to overweight patients. A total of 346 overweight Chinese people patients ages 18-81 years were involved in this study. Their levels of fasting glucose (fs-GLU), blood lipids, and hepatic and renal functions were measured and analyzed by multiple linear regression (MLR). Based the MLR results, we developed a back propagation artificial neural network (BP-ANN) model by selecting tansig as the transfer function of the hidden layers nodes, and purelin for the output layer nodes, with training goal of 0.5×10(-5). There was significant correlation between fs-GLU with age, BMI, and blood biochemical indexes (P<0.05). The results of MLR analysis indicated that age, fasting alanine transaminase (fs-ALT), blood urea nitrogen (fs-BUN), total protein (fs-TP), uric acid (fs-BUN), and BMI are 6 independent variables related to fs-GLU. Based on these parameters, the BP-ANN model was performed well and reached high prediction accuracy when training 1 000 epoch (R=0.9987). The level of fs-GLU was predictable using the proposed BP-ANN model based on 6 related parameters (age, fs-ALT, fs-BUN, fs-TP, fs-UA and BMI) in overweight patients. © Georg Thieme Verlag KG Stuttgart · New York.
Salleh, Faridah Hani Mohamed; Zainudin, Suhaila; Arif, Shereena M
2017-01-01
Gene regulatory network (GRN) reconstruction is the process of identifying regulatory gene interactions from experimental data through computational analysis. One of the main reasons for the reduced performance of previous GRN methods had been inaccurate prediction of cascade motifs. Cascade error is defined as the wrong prediction of cascade motifs, where an indirect interaction is misinterpreted as a direct interaction. Despite the active research on various GRN prediction methods, the discussion on specific methods to solve problems related to cascade errors is still lacking. In fact, the experiments conducted by the past studies were not specifically geared towards proving the ability of GRN prediction methods in avoiding the occurrences of cascade errors. Hence, this research aims to propose Multiple Linear Regression (MLR) to infer GRN from gene expression data and to avoid wrongly inferring of an indirect interaction (A → B → C) as a direct interaction (A → C). Since the number of observations of the real experiment datasets was far less than the number of predictors, some predictors were eliminated by extracting the random subnetworks from global interaction networks via an established extraction method. In addition, the experiment was extended to assess the effectiveness of MLR in dealing with cascade error by using a novel experimental procedure that had been proposed in this work. The experiment revealed that the number of cascade errors had been very minimal. Apart from that, the Belsley collinearity test proved that multicollinearity did affect the datasets used in this experiment greatly. All the tested subnetworks obtained satisfactory results, with AUROC values above 0.5.
Reflexion on linear regression trip production modelling method for ensuring good model quality
Suprayitno, Hitapriya; Ratnasari, Vita
2017-11-01
Transport Modelling is important. For certain cases, the conventional model still has to be used, in which having a good trip production model is capital. A good model can only be obtained from a good sample. Two of the basic principles of a good sampling is having a sample capable to represent the population characteristics and capable to produce an acceptable error at a certain confidence level. It seems that this principle is not yet quite understood and used in trip production modeling. Therefore, investigating the Trip Production Modelling practice in Indonesia and try to formulate a better modeling method for ensuring the Model Quality is necessary. This research result is presented as follows. Statistics knows a method to calculate span of prediction value at a certain confidence level for linear regression, which is called Confidence Interval of Predicted Value. The common modeling practice uses R2 as the principal quality measure, the sampling practice varies and not always conform to the sampling principles. An experiment indicates that small sample is already capable to give excellent R2 value and sample composition can significantly change the model. Hence, good R2 value, in fact, does not always mean good model quality. These lead to three basic ideas for ensuring good model quality, i.e. reformulating quality measure, calculation procedure, and sampling method. A quality measure is defined as having a good R2 value and a good Confidence Interval of Predicted Value. Calculation procedure must incorporate statistical calculation method and appropriate statistical tests needed. A good sampling method must incorporate random well distributed stratified sampling with a certain minimum number of samples. These three ideas need to be more developed and tested.
Charles K Fisher
Full Text Available Human associated microbial communities exert tremendous influence over human health and disease. With modern metagenomic sequencing methods it is now possible to follow the relative abundance of microbes in a community over time. These microbial communities exhibit rich ecological dynamics and an important goal of microbial ecology is to infer the ecological interactions between species directly from sequence data. Any algorithm for inferring ecological interactions must overcome three major obstacles: 1 a correlation between the abundances of two species does not imply that those species are interacting, 2 the sum constraint on the relative abundances obtained from metagenomic studies makes it difficult to infer the parameters in timeseries models, and 3 errors due to experimental uncertainty, or mis-assignment of sequencing reads into operational taxonomic units, bias inferences of species interactions due to a statistical problem called "errors-in-variables". Here we introduce an approach, Learning Interactions from MIcrobial Time Series (LIMITS, that overcomes these obstacles. LIMITS uses sparse linear regression with boostrap aggregation to infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested LIMITS on synthetic data and showed that it could reliably infer the topology of the inter-species ecological interactions. We then used LIMITS to characterize the species interactions in the gut microbiomes of two individuals and found that the interaction networks varied significantly between individuals. Furthermore, we found that the interaction networks of the two individuals are dominated by distinct "keystone species", Bacteroides fragilis and Bacteroided stercosis, that have a disproportionate influence on the structure of the gut microbiome even though they are only found in moderate abundance. Based on our results, we hypothesize that the abundances of certain keystone species may be responsible for individuality in
Stella Crosara Lopes
2009-04-01
Full Text Available The purpose of this study was to evaluate the metal-ceramic bond strength (MCBS of 6 metal-ceramic pairs (2 Ni-Cr alloys and 1 Pd-Ag alloy with 2 dental ceramics and correlate the MCBS values with the differences between the coefficients of linear thermal expansion (CTEs of the metals and ceramics. Verabond (VB Ni-Cr-Be alloy, Verabond II (VB2, Ni-Cr alloy, Pors-on 4 (P, Pd-Ag alloy, and IPS (I and Duceram (D ceramics were used for the MCBS test and dilatometric test. Forty-eight ceramic rings were built around metallic rods (3.0 mm in diameter and 70.0 mm in length made from the evaluated alloys. The rods were subsequently embedded in gypsum cast in order to perform a tensile load test, which enabled calculating the CMBS. Five specimens (2.0 mm in diameter and 12.0 mm in length of each material were made for the dilatometric test. The chromel-alumel thermocouple required for the test was welded into the metal test specimens and inserted into the ceramics. ANOVA and Tukey's test revealed significant differences (p=0.01 for the MCBS test results (MPa, with PI showing higher MCBS (67.72 than the other pairs, which did not present any significant differences. The CTE (10-6 oC-1 differences were: VBI (0.54, VBD (1.33, VB2I (-0.14, VB2D (0.63, PI (1.84 and PD (2.62. Pearson's correlation test (r=0.17 was performed to evaluate of correlation between MCBS and CTE differences. Within the limitations of this study and based on the obtained results, there was no correlation between MCBS and CTE differences for the evaluated metal-ceramic pairs.
Lopes, Stella Crosara; Pagnano, Valéria Oliveira; Rollo, João Manuel Domingos de Almeida; Leal, Mônica Barbosa; Bezzon, Osvaldo Luiz
2009-01-01
The purpose of this study was to evaluate the metal-ceramic bond strength (MCBS) of 6 metal-ceramic pairs (2 Ni-Cr alloys and 1 Pd-Ag alloy with 2 dental ceramics) and correlate the MCBS values with the differences between the coefficients of linear thermal expansion (CTEs) of the metals and ceramics. Verabond (VB) Ni-Cr-Be alloy, Verabond II (VB2), Ni-Cr alloy, Pors-on 4 (P), Pd-Ag alloy, and IPS (I) and Duceram (D) ceramics were used for the MCBS test and dilatometric test. Forty-eight ceramic rings were built around metallic rods (3.0 mm in diameter and 70.0 mm in length) made from the evaluated alloys. The rods were subsequently embedded in gypsum cast in order to perform a tensile load test, which enabled calculating the CMBS. Five specimens (2.0 mm in diameter and 12.0 mm in length) of each material were made for the dilatometric test. The chromel-alumel thermocouple required for the test was welded into the metal test specimens and inserted into the ceramics. ANOVA and Tukey's test revealed significant differences (p=0.01) for the MCBS test results (MPa), with PI showing higher MCBS (67.72) than the other pairs, which did not present any significant differences. The CTE (10(-6) oC(-1)) differences were: VBI (0.54), VBD (1.33), VB2I (-0.14), VB2D (0.63), PI (1.84) and PD (2.62). Pearson's correlation test (r=0.17) was performed to evaluate of correlation between MCBS and CTE differences. Within the limitations of this study and based on the obtained results, there was no correlation between MCBS and CTE differences for the evaluated metal-ceramic pairs.
Afantitis, Antreas; Melagraki, Georgia; Sarimveis, Haralambos; Koutentis, Panayiotis A; Markopoulos, John; Igglessi-Markopoulou, Olga
2006-08-01
A quantitative-structure activity relationship was obtained by applying Multiple Linear Regression Analysis to a series of 80 1-[2-hydroxyethoxy-methyl]-6-(phenylthio) thymine (HEPT) derivatives with significant anti-HIV activity. For the selection of the best among 37 different descriptors, the Elimination Selection Stepwise Regression Method (ES-SWR) was utilized. The resulting QSAR model (R (2) (CV) = 0.8160; S (PRESS) = 0.5680) proved to be very accurate both in training and predictive stages.
Leif E. Peterson
1997-11-01
Full Text Available A computer program for multifactor relative risks, confidence limits, and tests of hypotheses using regression coefficients and a variance-covariance matrix obtained from a previous additive or multiplicative regression analysis is described in detail. Data used by the program can be stored and input from an external disk-file or entered via the keyboard. The output contains a list of the input data, point estimates of single or joint effects, confidence intervals and tests of hypotheses based on a minimum modified chi-square statistic. Availability of the program is also discussed.
Evaluating Non-Linear Regression Models in Analysis of Persian Walnut Fruit Growth
I. Karamatlou
2016-02-01
Full Text Available Introduction: Persian walnut (Juglans regia L. is a large, wind-pollinated, monoecious, dichogamous, long lived, perennial tree cultivated for its high quality wood and nuts throughout the temperate regions of the world. Growth model methodology has been widely used in the modeling of plant growth. Mathematical models are important tools to study the plant growth and agricultural systems. These models can be applied for decision-making anddesigning management procedures in horticulture. Through growth analysis, planning for planting systems, fertilization, pruning operations, harvest time as well as obtaining economical yield can be more accessible.Non-linear models are more difficult to specify and estimate than linear models. This research was aimed to studynon-linear regression models based on data obtained from fruit weight, length and width. Selecting the best models which explain that fruit inherent growth pattern of Persian walnut was a further goal of this study. Materials and Methods: The experimental material comprising 14 Persian walnut genotypes propagated by seed collected from a walnut orchard in Golestan province, Minoudasht region, Iran, at latitude 37◦04’N; longitude 55◦32’E; altitude 1060 m, in a silt loam soil type. These genotypes were selected as a representative sampling of the many walnut genotypes available throughout the Northeastern Iran. The age range of walnut trees was 30 to 50 years. The annual mean temperature at the location is16.3◦C, with annual mean rainfall of 690 mm.The data used here is the average of walnut fresh fruit and measured withgram/millimeter/day in2011.According to the data distribution pattern, several equations have been proposed to describesigmoidal growth patterns. Here, we used double-sigmoid and logistic–monomolecular models to evaluate fruit growth based on fruit weight and4different regression models in cluding Richards, Gompertz, Logistic and Exponential growth for evaluation
Campra, Pablo; Morales, Maria
2016-01-01
The magnitude of the trends of environmental and climatic changes is mostly derived from the slopes of the linear trends using ordinary least-square fitting. An alternative flexible fitting model, piecewise regression, has been applied here to surface air temperature records in southeastern Spain for the recent warming period (1973–2014) to gain accuracy in the description of the inner structure of change, dividing the time series into linear segments with different slopes. Breakpoint y...
Correlated linear response calculations of the C6 dispersion coefficients of hydrogen halides
Sauer, S. P. A.; Paidarová, Ivana
2007-01-01
Roč. 3, 2-4 (2007), s. 399-421 ISSN 1574-0404 R&D Projects: GA AV ČR IAA401870702 Institutional research plan: CEZ:AV0Z40400503 Keywords : hydrogen halides * C6 dospersion coefficients * van der Waals coefficients * polarizability at imaginary frequences * SOPPA Subject RIV: CF - Physical ; Theoretical Chemistry
Nakanishi, Koichi; Kogure, Akinori; Fujii, Takenao; Kokawa, Ryohei; Deuchi, Keiji; Kuwana, Ritsuko; Takamatsu, Hiromu
2013-10-09
If a fixed stress is applied to the three-dimensional z-axis of a solid material, followed by heating, the amount of thermal expansion increases according to a fixed coefficient of thermal expansion. When expansion is plotted against temperature, the transition temperature at which the physical properties of the material change is at the apex of the curve. The composition of a microbial cell depends on the species and condition of the cell; consequently, the rate of thermal expansion and the transition temperature also depend on the species and condition of the cell. We have developed a method for measuring the coefficient of thermal expansion and the transition temperature of cells using a nano thermal analysis system in order to study the physical nature of the cells. The tendency was seen that among vegetative cells, the Gram-negative Escherichia coli and Pseudomonas aeruginosa have higher coefficients of linear expansion and lower transition temperatures than the Gram-positive Staphylococcus aureus and Bacillus subtilis. On the other hand, spores, which have low water content, overall showed lower coefficients of linear expansion and higher transition temperatures than vegetative cells. Comparing these trends to non-microbial materials, vegetative cells showed phenomenon similar to plastics and spores showed behaviour similar to metals with regards to the coefficient of liner thermal expansion. We show that vegetative cells occur phenomenon of similar to plastics and spores to metals with regard to the coefficient of liner thermal expansion. Cells may be characterized by the coefficient of linear expansion as a physical index; the coefficient of linear expansion may also characterize cells structurally since it relates to volumetric changes, surface area changes, the degree of expansion of water contained within the cell, and the intensity of the internal stress on the cellular membrane. The coefficient of linear expansion holds promise as a new index for
Hu, L; Zhang, Z G; Mouraux, A; Iannetti, G D
2015-05-01
Transient sensory, motor or cognitive event elicit not only phase-locked event-related potentials (ERPs) in the ongoing electroencephalogram (EEG), but also induce non-phase-locked modulations of ongoing EEG oscillations. These modulations can be detected when single-trial waveforms are analysed in the time-frequency domain, and consist in stimulus-induced decreases (event-related desynchronization, ERD) or increases (event-related synchronization, ERS) of synchrony in the activity of the underlying neuronal populations. ERD and ERS reflect changes in the parameters that control oscillations in neuronal networks and, depending on the frequency at which they occur, represent neuronal mechanisms involved in cortical activation, inhibition and binding. ERD and ERS are commonly estimated by averaging the time-frequency decomposition of single trials. However, their trial-to-trial variability that can reflect physiologically-important information is lost by across-trial averaging. Here, we aim to (1) develop novel approaches to explore single-trial parameters (including latency, frequency and magnitude) of ERP/ERD/ERS; (2) disclose the relationship between estimated single-trial parameters and other experimental factors (e.g., perceived intensity). We found that (1) stimulus-elicited ERP/ERD/ERS can be correctly separated using principal component analysis (PCA) decomposition with Varimax rotation on the single-trial time-frequency distributions; (2) time-frequency multiple linear regression with dispersion term (TF-MLRd) enhances the signal-to-noise ratio of ERP/ERD/ERS in single trials, and provides an unbiased estimation of their latency, frequency, and magnitude at single-trial level; (3) these estimates can be meaningfully correlated with each other and with other experimental factors at single-trial level (e.g., perceived stimulus intensity and ERP magnitude). The methods described in this article allow exploring fully non-phase-locked stimulus-induced cortical
Yan, Jun; Huang, Jian-Hua; He, Min; Lu, Hong-Bing; Yang, Rui; Kong, Bo; Xu, Qing-Song; Liang, Yi-Zeng
2013-08-01
Retention indices for frequently reported compounds of plant essential oils on three different stationary phases were investigated. Multivariate linear regression, partial least squares, and support vector machine combined with a new variable selection approach called random-frog recently proposed by our group, were employed to model quantitative structure-retention relationships. Internal and external validations were performed to ensure the stability and predictive ability. All the three methods could obtain an acceptable model, and the optimal results by support vector machine based on a small number of informative descriptors with the square of correlation coefficient for cross validation, values of 0.9726, 0.9759, and 0.9331 on the dimethylsilicone stationary phase, the dimethylsilicone phase with 5% phenyl groups, and the PEG stationary phase, respectively. The performances of two variable selection approaches, random-frog and genetic algorithm, are compared. The importance of the variables was found to be consistent when estimated from correlation coefficients in multivariate linear regression equations and selection probability in model spaces. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
vahid Rezaverdinejad
2017-01-01
important models to estimate ETc in greenhouse. The inputs of these models are net radiation, temperature, day after planting and air vapour pressure deficit (or relative humidity. Materials and Methods: In this study, daily ETc of reference crop, greenhouse tomato and cucumber crops were measured using lysimeter method in Urmia region. Several linear, nonlinear regressions and artificial neural networks were considered for ETc modelling in greenhouse. For this purpose, the effective meteorological parameters on ETc process includes: air temperature (T, air humidity (RH, air pressure (P, air vapour pressure deficit (VPD, day after planting (N and greenhouse net radiation (SR were considered and measured. According to the goodness of fit, different models of artificial neural networks and regression were compared and evaluated. Furthermore, based on partial derivatives of regression models, sensitivity analysis was conducted. The accuracy and performance of the employed models was judged by ten statistical indices namely root mean square error (RMSE, normalized root mean square error (NRMSE and coefficient of determination (R2. Results and Discussion: Based on the results, the most accurate regression model to reference ETc prediction was obtained three variables exponential function of VPD, RH and SR with RMSE=0.378 mm day-1. The RMSE of optimal artificial neural network to reference ET prediction for train and test data sets were obtained 0.089 and 0.365 mm day-1, respectively. The performance of logarithmic and exponential functions to prediction of cucumber ETc were proper, with high dependent variables especially, and the most accurate regression model to cucumber ET prediction was obtained for exponential function of five variables: VPD, N, T, RH and SR with RMSE=0.353 mm day-1. In addition, for tomato ET prediction, the most accurate regression model was obtained for exponential function of four variables: VPD, N, RH and SR with RMSE= 0.329 mm day-1. The best
Isolating and Examining Sources of Suppression and Multicollinearity in Multiple Linear Regression
Beckstead, Jason W.
2012-01-01
The presence of suppression (and multicollinearity) in multiple regression analysis complicates interpretation of predictor-criterion relationships. The mathematical conditions that produce suppression in regression analysis have received considerable attention in the methodological literature but until now nothing in the way of an analytic…
Krasikova, Dina V; Le, Huy; Bachura, Eric
2018-01-22
To address a long-standing concern regarding a gap between organizational science and practice, scholars called for more intuitive and meaningful ways of communicating research results to users of academic research. In this article, we develop a common language effect size index (CLβ) that can help translate research results to practice. We demonstrate how CLβ can be computed and used to interpret the effects of continuous and categorical predictors in multiple linear regression models. We also elaborate on how the proposed CLβ index is computed and used to interpret interactions and nonlinear effects in regression models. In addition, we test the robustness of the proposed index to violations of normality and provide means for computing standard errors and constructing confidence intervals around its estimates. (PsycINFO Database Record (c) 2018 APA, all rights reserved).
Rachid Darnag
2017-02-01
Full Text Available Support vector machines (SVM represent one of the most promising Machine Learning (ML tools that can be applied to develop a predictive quantitative structure–activity relationship (QSAR models using molecular descriptors. Multiple linear regression (MLR and artificial neural networks (ANNs were also utilized to construct quantitative linear and non linear models to compare with the results obtained by SVM. The prediction results are in good agreement with the experimental value of HIV activity; also, the results reveal the superiority of the SVM over MLR and ANN model. The contribution of each descriptor to the structure–activity relationships was evaluated.
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D; Keesman, K.J.; Zwart, Heiko J.
In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D.; Keesman, K.J.; Zwart, H.
2006-01-01
Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state
Aniela Balacescu; Marian Zaharia
2011-01-01
This paper aims to examine the causal relationship between GDP and final consumption. The authors used linear regression model in which GDP is considered variable results, and final consumption variable factor. In drafting article we used Excel software application that is a modern computing and statistical data analysis.
Kwan, Johnny S. H.; Kung, Annie W. C.; Sham, Pak C.
2011-01-01
Selective genotyping can increase power in quantitative trait association. One example of selective genotyping is two-tail extreme selection, but simple linear regression analysis gives a biased genetic effect estimate. Here, we present a simple correction for the bias. © The Author(s) 2011.
Fruehwirth, R.
1993-01-01
We present an estimation procedure of the error components in a linear regression model with multiple independent stochastic error contributions. After solving the general problem we apply the results to the estimation of the actual trajectory in track fitting with multiple scattering. (orig.)
Corsetti, James A.; Green, William E.; Ellis, Jonathan D.; Schmidt, Greg R.; Moore, Duncan T.
2017-01-01
A system combining an interferometer with an environmental chamber for measuring both coefficient of thermal expansion (CTE) and temperature-dependent refractive index (dn/dT) simultaneously is presented. The operation and measurement results of this instrument are discussed.
Sinev, Leonid S.; Petrov, Ivan D.
2017-01-01
Processing results of measurements of linear thermal expansion coefficients and linear thermal expansion of two brands of borosilicate glasses --- LK5 and Borofloat 33 --- are presented. The linear thermal expansion of glass samples have been determined in the temperature range 130 to 800 K (minus 143 to 526 $\\deg$C) using thermomechanical analyzer TMA7100. Relative imprecision of indirectly measured linear thermal expansion coefficients and linear thermal expansion of both glass brands is le...
Parker, Peter A.; Geoffrey, Vining G.; Wilson, Sara R.; Szarka, John L., III; Johnson, Nels G.
2010-01-01
The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.
Chen, Baojiang; Qin, Jing
2014-05-10
In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study. Copyright © 2013 John Wiley & Sons, Ltd.
Interpretation of commonly used statistical regression models.
Kasza, Jessica; Wolfe, Rory
2014-01-01
A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.
Boping Li
2015-01-01
Full Text Available At present, studies on the surface tension of air tunnel terrazzo under wind load and how regularly it is affected by temperature are relatively less, and the measured results of the thermal expansion coefficient of terrazzo have not yet been given. In this paper, based on the top terrazzo surface structure of the inner wall of the wind tunnel, the tensile performance tests of terrazzo surface layer are conducted, while the thermal expansion coefficient of the six terrazzo test blocks were tested. The tests and analysis show that the construction of terrazzo surface, based on the proposed construction process, can effectively guarantee the reliable cement performance for the binding layer between mortar and concrete base layer, terrazzo surface layer and the cement mortar layer. And the thermal expansion coefficient of terrazzo can be valued at 1.06e-5/ºC.
Sidik, S. M.
1975-01-01
Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.
Coskuntuncel, Orkun
2013-01-01
The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…
Christiansen, Bo
2015-04-01
Linear regression methods are without doubt the most used approaches to describe and predict data in the physical sciences. They are often good first order approximations and they are in general easier to apply and interpret than more advanced methods. However, even the properties of univariate regression can lead to debate over the appropriateness of various models as witnessed by the recent discussion about climate reconstruction methods. Before linear regression is applied important choices have to be made regarding the origins of the noise terms and regarding which of the two variables under consideration that should be treated as the independent variable. These decisions are often not easy to make but they may have a considerable impact on the results. We seek to give a unified probabilistic - Bayesian with flat priors - treatment of univariate linear regression and prediction by taking, as starting point, the general errors-in-variables model (Christiansen, J. Clim., 27, 2014-2031, 2014). Other versions of linear regression can be obtained as limits of this model. We derive the likelihood of the model parameters and predictands of the general errors-in-variables model by marginalizing over the nuisance parameters. The resulting likelihood is relatively simple and easy to analyze and calculate. The well known unidentifiability of the errors-in-variables model is manifested as the absence of a well-defined maximum in the likelihood. However, this does not mean that probabilistic inference can not be made; the marginal likelihoods of model parameters and the predictands have, in general, well-defined maxima. We also include a probabilistic version of classical calibration and show how it is related to the errors-in-variables model. The results are illustrated by an example from the coupling between the lower stratosphere and the troposphere in the Northern Hemisphere winter.
Endogenous glucose production from infancy to adulthood: a non-linear regression model
Huidekoper, Hidde H.; Ackermans, Mariëtte T.; Ruiter, An F. C.; Sauerwein, Hans P.; Wijburg, Frits A.
2014-01-01
To construct a regression model for endogenous glucose production (EGP) as a function of age, and compare this with glucose supplementation using commonly used dextrose-based saline solutions at fluid maintenance rate in children. A model was constructed based on EGP data, as quantified by
Weighted linear regression using D2H and D2 as the independent variables
Hans T. Schreuder; Michael S. Williams
1998-01-01
Several error structures for weighted regression equations used for predicting volume were examined for 2 large data sets of felled and standing loblolly pine trees (Pinus taeda L.). The generally accepted model with variance of error proportional to the value of the covariate squared ( D2H = diameter squared times height or D...
Fan, Xitao; Wang, Lin
The Monte Carlo study compared the performance of predictive discriminant analysis (PDA) and that of logistic regression (LR) for the two-group classification problem. Prior probabilities were used for classification, but the cost of misclassification was assumed to be equal. The study used a fully crossed three-factor experimental design (with…
NetRaVE: constructing dependency networks using sparse linear regression
Phatak, A.; Kiiveri, H.; Clemmensen, Line Katrine Harder
2010-01-01
NetRaVE is a small suite of R functions for generating dependency networks using sparse regression methods. Such networks provide an alternative to interpreting 'top n lists' of genes arising out of an analysis of microarray data, and they provide a means of organizing and visualizing the resulting...
Lorenzo-Seva, Urbano; Ferrando, Pere J
2011-03-01
We provide an SPSS program that implements currently recommended techniques and recent developments for selecting variables in multiple linear regression analysis via the relative importance of predictors. The approach consists of: (1) optimally splitting the data for cross-validation, (2) selecting the final set of predictors to be retained in the equation regression, and (3) assessing the behavior of the chosen model using standard indices and procedures. The SPSS syntax, a short manual, and data files related to this article are available as supplemental materials from brm.psychonomic-journals.org/content/supplemental.
Bhamidipati, Ravi Kanth; Syed, Muzeeb; Mullangi, Ramesh; Srinivas, Nuggehally
2018-02-01
1. Dalbavancin, a lipoglycopeptide, is approved for treating gram-positive bacterial infections. Area under plasma concentration versus time curve (AUC inf ) of dalbavancin is a key parameter and AUC inf /MIC ratio is a critical pharmacodynamic marker. 2. Using end of intravenous infusion concentration (i.e. C max ) C max versus AUC inf relationship for dalbavancin was established by regression analyses (i.e. linear, log-log, log-linear and power models) using 21 pairs of subject data. 3. The predictions of the AUC inf were performed using published C max data by application of regression equations. The quotient of observed/predicted values rendered fold difference. The mean absolute error (MAE)/root mean square error (RMSE) and correlation coefficient (r) were used in the assessment. 4. MAE and RMSE values for the various models were comparable. The C max versus AUC inf exhibited excellent correlation (r > 0.9488). The internal data evaluation showed narrow confinement (0.84-1.14-fold difference) with a RMSE models predicted AUC inf with a RMSE of 3.02-27.46% with fold difference largely contained within 0.64-1.48. 5. Regardless of the regression models, a single time point strategy of using C max (i.e. end of 30-min infusion) is amenable as a prospective tool for predicting AUC inf of dalbavancin in patients.
Regression Is a Univariate General Linear Model Subsuming Other Parametric Methods as Special Cases.
Vidal, Sherry
Although the concept of the general linear model (GLM) has existed since the 1960s, other univariate analyses such as the t-test and the analysis of variance models have remained popular. The GLM produces an equation that minimizes the mean differences of independent variables as they are related to a dependent variable. From a computer printout…
Kim, J. Y.; Shin, C. H.; Kim, J. K.; Lee, J. K.; Park, Y. J.
2003-01-01
The variation transitions of the inventories for the liquid radwaste system and the radioactive gas have being released in containment, and their predictive values according to the operation histories of Yonggwang(YGN) 3 and 4 were analyzed by linear regression analysis methodology. The results show that the variation transitions of the inventories for those systems are linearly increasing according to the operation histories but the inventories released to the environment are considerably lower than the recommended values based on the FSAR suggestions. It is considered that some conservation were presented in the estimation methodology in preparing stage of FSAR
Kaneko, Hiromasa
2018-02-26
To develop a new ensemble learning method and construct highly predictive regression models in chemoinformatics and chemometrics, applicability domains (ADs) are introduced into the ensemble learning process of prediction. When estimating values of an objective variable using subregression models, only the submodels with ADs that cover a query sample, i.e., the sample is inside the model's AD, are used. By constructing submodels and changing a list of selected explanatory variables, the union of the submodels' ADs, which defines the overall AD, becomes large, and the prediction performance is enhanced for diverse compounds. By analyzing a quantitative structure-activity relationship data set and a quantitative structure-property relationship data set, it is confirmed that the ADs can be enlarged and the estimation performance of regression models is improved compared with traditional methods.
Linear Regression with a Randomly Censored Covariate: Application to an Alzheimer's Study.
Atem, Folefac D; Qian, Jing; Maye, Jacqueline E; Johnson, Keith A; Betensky, Rebecca A
2017-01-01
The association between maternal age of onset of dementia and amyloid deposition (measured by in vivo positron emission tomography (PET) imaging) in cognitively normal older offspring is of interest. In a regression model for amyloid, special methods are required due to the random right censoring of the covariate of maternal age of onset of dementia. Prior literature has proposed methods to address the problem of censoring due to assay limit of detection, but not random censoring. We propose imputation methods and a survival regression method that do not require parametric assumptions about the distribution of the censored covariate. Existing imputation methods address missing covariates, but not right censored covariates. In simulation studies, we compare these methods to the simple, but inefficient complete case analysis, and to thresholding approaches. We apply the methods to the Alzheimer's study.
SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression
Flores, Salvador
2015-01-01
This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the Least Trimmed Squares Estimator (LTSE) for robust regression. The computation of the LTSE is a challenging subset selection problem involving a nonlinear program with continuous and binary variables, linked in a highly nonlinear fashion. The selection of a ...
Nakagawa, Shinichi; Johnson, Paul C D; Schielzeth, Holger
2017-09-01
The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called [Formula: see text] for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments. © 2017 The Author(s).
Miguel-Hurtado, Oscar; Guest, Richard; Stevenage, Sarah V; Neil, Greg J; Black, Sue
2016-01-01
Understanding the relationship between physiological measurements from human subjects and their demographic data is important within both the biometric and forensic domains. In this paper we explore the relationship between measurements of the human hand and a range of demographic features. We assess the ability of linear regression and machine learning classifiers to predict demographics from hand features, thereby providing evidence on both the strength of relationship and the key features underpinning this relationship. Our results show that we are able to predict sex, height, weight and foot size accurately within various data-range bin sizes, with machine learning classification algorithms out-performing linear regression in most situations. In addition, we identify the features used to provide these relationships applicable across multiple applications.
1981-09-01
corresponds to the same square footage that consumed the electrical energy. 3. The basic assumptions of multiple linear regres- sion, as enumerated in...7. Data related to the sample of bases is assumed to be representative of bases in the population. Limitations Basic limitations on this research were... Ratemaking --Overview. Rand Report R-5894, Santa Monica CA, May 1977. Chatterjee, Samprit, and Bertram Price. Regression Analysis by Example. New York: John
Mihai, Maria; Popescu, I.V.
2002-01-01
In this paper we present a mathematical model that would describe the stability and instability conditions, respectively of the organs of human body assumed as a living cybernetic system with feedback. We tested the theoretical model on the following trace elements: Mn, Zn and As. The trace elements were determined from the nose-pharyngeal carcinoma. We utilise the linear approximation to describe the dependencies between the trace elements determined in the hair of the patient. We present the results graphically. (authors)
Lattice Designs in Standard and Simple Implicit Multi-linear Regression
Wooten, Rebecca D.
2016-01-01
Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the random error in the system without defining a subject response. Using lattice design Wooten shows that non-response analysis is a superior alternative rotation of the pyramidal relationship between random variables and parameter estimates in multi-linear r...
Delbari, Masoomeh; Sharifazari, Salman; Mohammadi, Ehsan
2018-02-01
The knowledge of soil temperature at different depths is important for agricultural industry and for understanding climate change. The aim of this study is to evaluate the performance of a support vector regression (SVR)-based model in estimating daily soil temperature at 10, 30 and 100 cm depth at different climate conditions over Iran. The obtained results were compared to those obtained from a more classical multiple linear regression (MLR) model. The correlation sensitivity for the input combinations and periodicity effect were also investigated. Climatic data used as inputs to the models were minimum and maximum air temperature, solar radiation, relative humidity, dew point, and the atmospheric pressure (reduced to see level), collected from five synoptic stations Kerman, Ahvaz, Tabriz, Saghez, and Rasht located respectively in the hyper-arid, arid, semi-arid, Mediterranean, and hyper-humid climate conditions. According to the results, the performance of both MLR and SVR models was quite well at surface layer, i.e., 10-cm depth. However, SVR performed better than MLR in estimating soil temperature at deeper layers especially 100 cm depth. Moreover, both models performed better in humid climate condition than arid and hyper-arid areas. Further, adding a periodicity component into the modeling process considerably improved the models' performance especially in the case of SVR.
Zhang, Xin; Liu, Pan; Chen, Yuguang; Bai, Lu; Wang, Wei
2014-01-01
The primary objective of this study was to identify whether the frequency of traffic conflicts at signalized intersections can be modeled. The opposing left-turn conflicts were selected for the development of conflict predictive models. Using data collected at 30 approaches at 20 signalized intersections, the underlying distributions of the conflicts under different traffic conditions were examined. Different conflict-predictive models were developed to relate the frequency of opposing left-turn conflicts to various explanatory variables. The models considered include a linear regression model, a negative binomial model, and separate models developed for four traffic scenarios. The prediction performance of different models was compared. The frequency of traffic conflicts follows a negative binominal distribution. The linear regression model is not appropriate for the conflict frequency data. In addition, drivers behaved differently under different traffic conditions. Accordingly, the effects of conflicting traffic volumes on conflict frequency vary across different traffic conditions. The occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The use of conflict predictive models has potential to expand the uses of surrogate safety measures in safety estimation and evaluation.
Xiaoyan Yang
2018-04-01
Full Text Available The Advanced Spaceborne Thermal-Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM is important to a wide range of geographical and environmental studies. Its accuracy, to some extent associated with land-use types reflecting topography, vegetation coverage, and human activities, impacts the results and conclusions of these studies. In order to improve the accuracy of ASTER GDEM prior to its application, we investigated ASTER GDEM errors based on individual land-use types and proposed two linear regression calibration methods, one considering only land use-specific errors and the other considering the impact of both land-use and topography. Our calibration methods were tested on the coastal prefectural city of Lianyungang in eastern China. Results indicate that (1 ASTER GDEM is highly accurate for rice, wheat, grass and mining lands but less accurate for scenic, garden, wood and bare lands; (2 despite improvements in ASTER GDEM2 accuracy, multiple linear regression calibration requires more data (topography and a relatively complex calibration process; (3 simple linear regression calibration proves a practicable and simplified means to systematically investigate and improve the impact of land-use on ASTER GDEM accuracy. Our method is applicable to areas with detailed land-use data based on highly accurate field-based point-elevation measurements.
Mar'yanov, B.M.; Shumar, S.V.; Gavrilenko, M.A.
1994-01-01
A method for the computer processing of the curves of potentiometric differential titration using the precipitation reactions is developed. This method is based on transformation of the titration curve into a line of multiphase regression, whose parameters determine the equivalence points and the solubility products of the formed precipitates. The computational algorithm is tested using experimental curves for the titration of solutions containing Hg(2) and Cd(2) by the solution of sodium diethyldithiocarbamate. The random errors (RSD) for the titration of 1x10 -4 M solutions are in the range of 3-6%. 7 refs.; 2 figs.; 1 tab
Yano, Kentaro; Mita, Suzune; Morimoto, Kaori; Haraguchi, Tamami; Arakawa, Hiroshi; Yoshida, Miyako; Yamashita, Fumiyoshi; Uchida, Takahiro; Ogihara, Takuo
2015-09-01
P-glycoprotein (P-gp) regulates absorption of many drugs in the gastrointestinal tract and their accumulation in tumor tissues, but the basis of substrate recognition by P-gp remains unclear. Bitter-tasting phenylthiocarbamide, which stimulates taste receptor 2 member 38 (T2R38), increases P-gp activity and is a substrate of P-gp. This led us to hypothesize that bitterness intensity might be a predictor of P-gp-inhibitor/substrate status. Here, we measured the bitterness intensity of a panel of P-gp substrates and nonsubstrates with various taste sensors, and used multiple linear regression analysis to examine the relationship between P-gp-inhibitor/substrate status and various physical properties, including intensity of bitter taste measured with the taste sensor. We calculated the first principal component analysis score (PC1) as the representative value of bitterness, as all taste sensor's outputs shared significant correlation. The P-gp substrates showed remarkably greater mean bitterness intensity than non-P-gp substrates. We found that Km value of P-gp substrates were correlated with molecular weight, log P, and PC1 value, and the coefficient of determination (R(2) ) of the linear regression equation was 0.63. This relationship might be useful as an aid to predict P-gp substrate status at an early stage of drug discovery. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association.
Chen, Qingxia; Ibrahim, Joseph G
2014-07-01
Multiple Imputation, Maximum Likelihood and Fully Bayesian methods are the three most commonly used model-based approaches in missing data problems. Although it is easy to show that when the responses are missing at random (MAR), the complete case analysis is unbiased and efficient, the aforementioned methods are still commonly used in practice for this setting. To examine the performance of and relationships between these three methods in this setting, we derive and investigate small sample and asymptotic expressions of the estimates and standard errors, and fully examine how these estimates are related for the three approaches in the linear regression model when the responses are MAR. We show that when the responses are MAR in the linear model, the estimates of the regression coefficients using these three methods are asymptotically equivalent to the complete case estimates under general conditions. One simulation and a real data set from a liver cancer clinical trial are given to compare the properties of these methods when the responses are MAR.
Ren, Y Y; Zhou, L C; Yang, L; Liu, P Y; Zhao, B W; Liu, H X
2016-09-01
The paper highlights the use of the logistic regression (LR) method in the construction of acceptable statistically significant, robust and predictive models for the classification of chemicals according to their aquatic toxic modes of action. Essentials accounting for a reliable model were all considered carefully. The model predictors were selected by stepwise forward discriminant analysis (LDA) from a combined pool of experimental data and chemical structure-based descriptors calculated by the CODESSA and DRAGON software packages. Model predictive ability was validated both internally and externally. The applicability domain was checked by the leverage approach to verify prediction reliability. The obtained models are simple and easy to interpret. In general, LR performs much better than LDA and seems to be more attractive for the prediction of the more toxic compounds, i.e. compounds that exhibit excess toxicity versus non-polar narcotic compounds and more reactive compounds versus less reactive compounds. In addition, model fit and regression diagnostics was done through the influence plot which reflects the hat-values, studentized residuals, and Cook's distance statistics of each sample. Overdispersion was also checked for the LR model. The relationships between the descriptors and the aquatic toxic behaviour of compounds are also discussed.
Abad, Cesar C C; Barros, Ronaldo V; Bertuzzi, Romulo; Gagliardi, João F L; Lima-Silva, Adriano E; Lambert, Mike I; Pires, Flavio O
2016-06-01
The aim of this study was to verify the power of VO 2max , peak treadmill running velocity (PTV), and running economy (RE), unadjusted or allometrically adjusted, in predicting 10 km running performance. Eighteen male endurance runners performed: 1) an incremental test to exhaustion to determine VO 2max and PTV; 2) a constant submaximal run at 12 km·h -1 on an outdoor track for RE determination; and 3) a 10 km running race. Unadjusted (VO 2max , PTV and RE) and adjusted variables (VO 2max 0.72 , PTV 0.72 and RE 0.60 ) were investigated through independent multiple regression models to predict 10 km running race time. There were no significant correlations between 10 km running time and either the adjusted or unadjusted VO 2max . Significant correlations (p 0.84 and power > 0.88. The allometrically adjusted predictive model was composed of PTV 0.72 and RE 0.60 and explained 83% of the variance in 10 km running time with a standard error of the estimate (SEE) of 1.5 min. The unadjusted model composed of a single PVT accounted for 72% of the variance in 10 km running time (SEE of 1.9 min). Both regression models provided powerful estimates of 10 km running time; however, the unadjusted PTV may provide an uncomplicated estimation.
Jaber, Abobaker M; Ismail, Mohd Tahir; Altaher, Alsaidi M
2014-01-01
This paper mainly forecasts the daily closing price of stock markets. We propose a two-stage technique that combines the empirical mode decomposition (EMD) with nonparametric methods of local linear quantile (LLQ). We use the proposed technique, EMD-LLQ, to forecast two stock index time series. Detailed experiments are implemented for the proposed method, in which EMD-LPQ, EMD, and Holt-Winter methods are compared. The proposed EMD-LPQ model is determined to be superior to the EMD and Holt-Winter methods in predicting the stock closing prices.
Cui, Haibo; Wei, Xiaomei; Huang, Yu; Hu, Bin; Fang, Yaping; Wang, Jia
2014-01-01
Among human influenza viruses, strain A/H3N2 accounts for over a quarter of a million deaths annually. Antigenic variants of these viruses often render current vaccinations ineffective and lead to repeated infections. In this study, a computational model was developed to predict antigenic variants of the A/H3N2 strain. First, 18 critical antigenic amino acids in the hemagglutinin (HA) protein were recognized using a scoring method combining phi (ϕ) coefficient and information entropy. Next, a prediction model was developed by integrating multiple linear regression method with eight types of physicochemical changes in critical amino acid positions. When compared to other three known models, our prediction model achieved the best performance not only on the training dataset but also on the commonly-used testing dataset composed of 31878 antigenic relationships of the H3N2 influenza virus.
Ghavami, Raoof; Najafi, Amir; Sajadi, Mohammad; Djannaty, Farhad
2008-09-01
In order to accurately simulate (13)C NMR spectra of hydroxy, polyhydroxy and methoxy substituted flavonoid a quantitative structure-property relationship (QSPR) model, relating atom-based calculated descriptors to (13)C NMR chemical shifts (ppm, TMS=0), is developed. A dataset consisting of 50 flavonoid derivatives was employed for the present analysis. A set of 417 topological, geometrical, and electronic descriptors representing various structural characteristics was calculated and separate multilinear QSPR models were developed between each carbon atom of flavonoid and the calculated descriptors. Genetic algorithm (GA) and multiple linear regression analysis (MLRA) were used to select the descriptors and to generate the correlation models. Analysis of the results revealed a correlation coefficient and root mean square error (RMSE) of 0.994 and 2.53ppm, respectively, for the prediction set.
A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients
Casas Pérez, Fernando; Chiralt Monleon, Cristina
2014-01-01
A perturbative procedure based on the Lie-Deprit algorithm of classical mechanics is proposed to compute analytic approximations to the fundamental matrix of linear di erential equations with periodic coe cients. These approximations reproduce the structure assured by the Floquet theorem. Alternatively, the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodic problem to an autonomous sys- tem and also to its characteristic ...
Wu Qingjie; Guo Kangxian; Liu Guanghui; Wu Jinghe
2013-01-01
Polaron effects on the linear and the nonlinear optical absorption coefficients and refractive index changes in cylindrical quantum dots with the radial parabolic potential and the z-direction linear potential with applied magnetic field are theoretically investigated. The optical absorption coefficients and refractive index changes are presented by using the compact-density-matrix approach and iterative method. Numerical calculations are presented for GaAs/AlGaAs. It is found that taking into account the electron-LO-phonon interaction, not only are the linear, the nonlinear and the total optical absorption coefficients and refractive index changes enhanced, but also the total optical absorption coefficients are more sensitive to the incident optical intensity. It is also found that no matter whether the electron-LO-phonon interaction is considered or not, the absorption coefficients and refractive index changes above are strongly dependent on the radial frequency, the magnetic field and the linear potential coefficient.
Comparison of Adaline and Multiple Linear Regression Methods for Rainfall Forecasting
Sutawinaya, IP; Astawa, INGA; Hariyanti, NKD
2018-01-01
Heavy rainfall can cause disaster, therefore need a forecast to predict rainfall intensity. Main factor that cause flooding is there is a high rainfall intensity and it makes the river become overcapacity. This will cause flooding around the area. Rainfall factor is a dynamic factor, so rainfall is very interesting to be studied. In order to support the rainfall forecasting, there are methods that can be used from Artificial Intelligence (AI) to statistic. In this research, we used Adaline for AI method and Regression for statistic method. The more accurate forecast result shows the method that used is good for forecasting the rainfall. Through those methods, we expected which is the best method for rainfall forecasting here.
Kargoll, Boris; Omidalizarandi, Mohammad; Loth, Ina; Paffenholz, Jens-André; Alkhatib, Hamza
2018-03-01
In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student's) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.
Hunt, Andrew P; Bach, Aaron J E; Borg, David N; Costello, Joseph T; Stewart, Ian B
2017-01-01
An accurate measure of core body temperature is critical for monitoring individuals, groups and teams undertaking physical activity in situations of high heat stress or prolonged cold exposure. This study examined the range in systematic bias of ingestible temperature sensors compared to a certified and traceable reference thermometer. A total of 119 ingestible temperature sensors were immersed in a circulated water bath at five water temperatures (TEMP A: 35.12 ± 0.60°C, TEMP B: 37.33 ± 0.56°C, TEMP C: 39.48 ± 0.73°C, TEMP D: 41.58 ± 0.97°C, and TEMP E: 43.47 ± 1.07°C) along with a certified traceable reference thermometer. Thirteen sensors (10.9%) demonstrated a systematic bias > ±0.1°C, of which 4 (3.3%) were > ± 0.5°C. Limits of agreement (95%) indicated that systematic bias would likely fall in the range of -0.14 to 0.26°C, highlighting that it is possible for temperatures measured between sensors to differ by more than 0.4°C. The proportion of sensors with systematic bias > ±0.1°C (10.9%) confirms that ingestible temperature sensors require correction to ensure their accuracy. An individualized linear correction achieved a mean systematic bias of 0.00°C, and limits of agreement (95%) to 0.00-0.00°C, with 100% of sensors achieving ±0.1°C accuracy. Alternatively, a generalized linear function (Corrected Temperature (°C) = 1.00375 × Sensor Temperature (°C) - 0.205549), produced as the average slope and intercept of a sub-set of 51 sensors and excluding sensors with accuracy outside ±0.5°C, reduced the systematic bias to Correction of sensor temperature to a reference thermometer by linear function eliminates this systematic bias (individualized functions) or ensures systematic bias is within ±0.1°C in 98% of the sensors (generalized function).
Andrew P. Hunt
2017-04-01
Full Text Available An accurate measure of core body temperature is critical for monitoring individuals, groups and teams undertaking physical activity in situations of high heat stress or prolonged cold exposure. This study examined the range in systematic bias of ingestible temperature sensors compared to a certified and traceable reference thermometer. A total of 119 ingestible temperature sensors were immersed in a circulated water bath at five water temperatures (TEMP A: 35.12 ± 0.60°C, TEMP B: 37.33 ± 0.56°C, TEMP C: 39.48 ± 0.73°C, TEMP D: 41.58 ± 0.97°C, and TEMP E: 43.47 ± 1.07°C along with a certified traceable reference thermometer. Thirteen sensors (10.9% demonstrated a systematic bias > ±0.1°C, of which 4 (3.3% were > ± 0.5°C. Limits of agreement (95% indicated that systematic bias would likely fall in the range of −0.14 to 0.26°C, highlighting that it is possible for temperatures measured between sensors to differ by more than 0.4°C. The proportion of sensors with systematic bias > ±0.1°C (10.9% confirms that ingestible temperature sensors require correction to ensure their accuracy. An individualized linear correction achieved a mean systematic bias of 0.00°C, and limits of agreement (95% to 0.00–0.00°C, with 100% of sensors achieving ±0.1°C accuracy. Alternatively, a generalized linear function (Corrected Temperature (°C = 1.00375 × Sensor Temperature (°C − 0.205549, produced as the average slope and intercept of a sub-set of 51 sensors and excluding sensors with accuracy outside ±0.5°C, reduced the systematic bias to < ±0.1°C in 98.4% of the remaining sensors (n = 64. In conclusion, these data show that using an uncalibrated ingestible temperature sensor may provide inaccurate data that still appears to be statistically, physiologically, and clinically meaningful. Correction of sensor temperature to a reference thermometer by linear function eliminates this systematic bias (individualized functions or ensures
Fang, Yu-Hua; Kao, Tsair; Liu, Ren-Shyan; Wu, Liang-Chih
2004-01-01
A novel statistical method, namely Regression-Estimated Input Function (REIF), is proposed in this study for the purpose of non-invasive estimation of the input function for fluorine-18 2-fluoro-2-deoxy-d-glucose positron emission tomography (FDG-PET) quantitative analysis. We collected 44 patients who had undergone a blood sampling procedure during their FDG-PET scans. First, we generated tissue time-activity curves of the grey matter and the whole brain with a segmentation technique for every subject. Summations of different intervals of these two curves were used as a feature vector, which also included the net injection dose. Multiple linear regression analysis was then applied to find the correlation between the input function and the feature vector. After a simulation study with in vivo data, the data of 29 patients were applied to calculate the regression coefficients, which were then used to estimate the input functions of the other 15 subjects. Comparing the estimated input functions with the corresponding real input functions, the averaged error percentages of the area under the curve and the cerebral metabolic rate of glucose (CMRGlc) were 12.13±8.85 and 16.60±9.61, respectively. Regression analysis of the CMRGlc values derived from the real and estimated input functions revealed a high correlation (r=0.91). No significant difference was found between the real CMRGlc and that derived from our regression-estimated input function (Student's t test, P>0.05). The proposed REIF method demonstrated good abilities for input function and CMRGlc estimation, and represents a reliable replacement for the blood sampling procedures in FDG-PET quantification. (orig.)
Pollock, D.; Kim, K.; Gunst, R.; Schucany, W.
1993-05-01
Linear estimation of cold magnetic field quality based on warm multipole measurements is being considered as a quality control method for SSC production magnet acceptance. To investigate prediction uncertainties associated with such an approach, axial-scan (Z-scan) magnetic measurements from SSC Prototype Collider Dipole Magnets (CDM's) have been studied. This paper presents a preliminary evaluation of the explanatory ability of warm measurement multipole variation on the prediction of cold magnet multipoles. Two linear estimation methods are presented: least-squares regression, which uses the assumption of fixed independent variable (xi) observations, and the measurement error model, which includes measurement error in the xi's. The influence of warm multipole measurement errors on predicted cold magnet multipole averages is considered. MSD QA is studying warm/cold correlation to answer several magnet quality control questions. How well do warm measurements predict cold (2kA) multipoles? Does sampling error significantly influence estimates of the linear coefficients (slope, intercept and residual standard error)? Is estimation error for the predicted cold magnet average small compared to typical variation along the Z-Axis? What fraction of the multipole RMS tolerance is accounted for by individual magnet prediction uncertainty?
Coelho, Lúcia H G; Gutz, Ivano G R
2006-03-15
A chemometric method for analysis of conductometric titration data was introduced to extend its applicability to lower concentrations and more complex acid-base systems. Auxiliary pH measurements were made during the titration to assist the calculation of the distribution of protonable species on base of known or guessed equilibrium constants. Conductivity values of each ionized or ionizable species possibly present in the sample were introduced in a general equation where the only unknown parameters were the total concentrations of (conjugated) bases and of strong electrolytes not involved in acid-base equilibria. All these concentrations were adjusted by a multiparametric nonlinear regression (NLR) method, based on the Levenberg-Marquardt algorithm. This first conductometric titration method with NLR analysis (CT-NLR) was successfully applied to simulated conductometric titration data and to synthetic samples with multiple components at concentrations as low as those found in rainwater (approximately 10 micromol L(-1)). It was possible to resolve and quantify mixtures containing a strong acid, formic acid, acetic acid, ammonium ion, bicarbonate and inert electrolyte with accuracy of 5% or better.
Zhang, Hanze; Huang, Yangxin; Wang, Wei; Chen, Henian; Langland-Orban, Barbara
2017-01-01
In longitudinal AIDS studies, it is of interest to investigate the relationship between HIV viral load and CD4 cell counts, as well as the complicated time effect. Most of common models to analyze such complex longitudinal data are based on mean-regression, which fails to provide efficient estimates due to outliers and/or heavy tails. Quantile regression-based partially linear mixed-effects models, a special case of semiparametric models enjoying benefits of both parametric and nonparametric models, have the flexibility to monitor the viral dynamics nonparametrically and detect the varying CD4 effects parametrically at different quantiles of viral load. Meanwhile, it is critical to consider various data features of repeated measurements, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution. In this research, we first establish a Bayesian joint models that accounts for all these data features simultaneously in the framework of quantile regression-based partially linear mixed-effects models. The proposed models are applied to analyze the Multicenter AIDS Cohort Study (MACS) data. Simulation studies are also conducted to assess the performance of the proposed methods under different scenarios.
Robi Yanto
2018-04-01
Full Text Available Tingginya aktivitas konsumsi yang dilakukan masyarakat berbanding lurus dengan meningkatnnya produksi sampah. Salah satu permasalahan tingginya produksi sampah yaitu rendahnya kesadaran masyarakat terhadap pengelolaan sampah. Hal ini merupakan masalah yang dihadapi di kota-kota besar. Sampah memberikan dampak negatif terhadap perubahan kondisi alam yang ada yaitu terjadinya polusi udara, air dan tanah yang mengakibatkan lingkungan menjadi tidak sehat. Kegiatan pengelolaan sampah melalui sosialisasi program 3R (Reduce, Reuse, Recycle tentang sampah, telah memberikan dampak yang maksimal terhadap kesadaran masyarakat tentang pentingnya lingkungan yang sehat. seiring dengan peningkatan jumlah penduduk memberikan dampak pada peningkatan produksi sampah. Sehingga membutuhkan lahan pembuangan sampah yang mencukupi dalam jangka panjang. Untuk mengatasi permasalahan tersebut maka dilakukan analisa data terhadap estimasi ketersediaan lahan pembuangan sampah dalam jangka panjang dengan menggunakan teknik data mining. dari hasil analisa data mining menggunakan algoritma regresi linear sederhana dengan memperhatikan pertumbuhan penduduk tahun 2018 sampai dengan 2025 sebesar 201484 jiwa, maka diketahui bahwa peningkatan sampah dari tahun 2018 sampai dengan tahun 2025 adalah 36.052,326 ton. Sehingga dari luas lahan 30000 M2 hanya tersediaan lahan pembuangan sampah sampai tahun 2025 sebesar 5.965,1 M2.
A componential model of human interaction with graphs: 1. Linear regression modeling
Gillan, Douglas J.; Lewis, Robert
1994-01-01
Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.
Linear thermal expansion coefficient of cast Fe-Ni invar and Fe-Ni-Co superinvar alloys
Ogorodnikova, O.M.; Chermenskaya, E.V.; Rabinovich, S.V.; Grachev, S.V.
1999-01-01
Cast invar alloys Fe-Ni (28-35 wt. % Ni) are investigated using metallography, dilatometry and X-ray methods as soon as the crystallization is completed and again after low-temperature treatment resulting in martensitic transformation in low nickel alloys. Nickel distribution in a cast superinvar Fe-32% Ni-4% Co is studied by means of X-ray spectrum microanalysis. The results obtained permit the correction of model concepts about cast invars and the estimate of a coefficient of linear expansion depending on phase composition and nickel microsegregation [ru
On Attainability of Optimal Solutions for Linear Elliptic Equations with Unbounded Coefficients
P. I. Kogut
2011-12-01
Full Text Available We study an optimal boundary control problem (OCP associated to a linear elliptic equation —div (Vj/ + A(xVy = f describing diffusion in a turbulent flow. The characteristic feature of this equation is the fact that, in applications, the stream matrix A(x = [a,ij(x]i,j=i,...,N is skew-symmetric, ац(х = —a,ji(x, measurable, and belongs to L -space (rather than L°°. An optimal solution to such problem can inherit a singular character of the original stream matrix A. We show that optimal solutions can be attainable by solutions of special optimal boundary control problems.
Paris, R.B.; Wood, A.D.
1984-11-01
The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper
Paulino Pérez
2010-09-01
Full Text Available The availability of dense molecular markers has made possible the use of genomic selection in plant and animal breeding. However, models for genomic selection pose several computational and statistical challenges and require specialized computer programs, not always available to the end user and not implemented in standard statistical software yet. The R-package BLR (Bayesian Linear Regression implements several statistical procedures (e.g., Bayesian Ridge Regression, Bayesian LASSO in a unified framework that allows including marker genotypes and pedigree data jointly. This article describes the classes of models implemented in the BLR package and illustrates their use through examples. Some challenges faced when applying genomic-enabled selection, such as model choice, evaluation of predictive ability through cross-validation, and choice of hyper-parameters, are also addressed.
Yu, Donghai; Du, Ruobing; Xiao, Ji-Chang
2016-07-05
Ninety-six acidic phosphorus-containing molecules with pKa 1.88 to 6.26 were collected and divided into training and test sets by random sampling. Structural parameters were obtained by density functional theory calculation of the molecules. The relationship between the experimental pKa values and structural parameters was obtained by multiple linear regression fitting for the training set, and tested with the test set; the R(2) values were 0.974 and 0.966 for the training and test sets, respectively. This regression equation, which quantitatively describes the influence of structural parameters on pKa , and can be used to predict pKa values of similar structures, is significant for the design of new acidic phosphorus-containing extractants. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Theobald, Roddy; Freeman, Scott
2014-01-01
Although researchers in undergraduate science, technology, engineering, and mathematics education are currently using several methods to analyze learning gains from pre- and posttest data, the most commonly used approaches have significant shortcomings. Chief among these is the inability to distinguish whether differences in learning gains are due to the effect of an instructional intervention or to differences in student characteristics when students cannot be assigned to control and treatment groups at random. Using pre- and posttest scores from an introductory biology course, we illustrate how the methods currently in wide use can lead to erroneous conclusions, and how multiple linear regression offers an effective framework for distinguishing the impact of an instructional intervention from the impact of student characteristics on test score gains. In general, we recommend that researchers always use student-level regression models that control for possible differences in student ability and preparation to estimate the effect of any nonrandomized instructional intervention on student performance.
Hsu, Ching-Chi; Lin, Jinn; Chao, Ching-Kong
2011-12-01
Optimizing the orthopaedic screws can greatly improve their biomechanical performances. However, a methodical design optimization approach requires a long time to search the best design. Thus, the surrogate objective functions of the orthopaedic screws should be accurately developed. To our knowledge, there is no study to evaluate the strengths and limitations of the surrogate methods in developing the objective functions of the orthopaedic screws. Three-dimensional finite element models for both the tibial locking screws and the spinal pedicle screws were constructed and analyzed. Then, the learning data were prepared according to the arrangement of the Taguchi orthogonal array, and the verification data were selected with use of a randomized selection. Finally, the surrogate objective functions were developed by using either the multiple linear regression or the artificial neural network. The applicability and accuracy of those surrogate methods were evaluated and discussed. The multiple linear regression method could successfully construct the objective function of the tibial locking screws, but it failed to develop the objective function of the spinal pedicle screws. The artificial neural network method showed a greater capacity of prediction in developing the objective functions for the tibial locking screws and the spinal pedicle screws than the multiple linear regression method. The artificial neural network method may be a useful option for developing the objective functions of the orthopaedic screws with a greater structural complexity. The surrogate objective functions of the orthopaedic screws could effectively decrease the time and effort required for the design optimization process. Copyright Â© 2010 Elsevier Ireland Ltd. All rights reserved.
Dong, J Q; Zhang, X Y; Wang, S Z; Jiang, X F; Zhang, K; Ma, G W; Wu, M Q; Li, H; Zhang, H
2018-01-01
Plasma very low-density lipoprotein (VLDL) can be used to select for low body fat or abdominal fat (AF) in broilers, but its correlation with AF is limited. We investigated whether any other biochemical indicator can be used in combination with VLDL for a better selective effect. Nineteen plasma biochemical indicators were measured in male chickens from the Northeast Agricultural University broiler lines divergently selected for AF content (NEAUHLF) in the fed state at 46 and 48 d of age. The average concentration of every parameter for the 2 d was used for statistical analysis. Levels of these 19 plasma biochemical parameters were compared between the lean and fat lines. The phenotypic correlations between these plasma biochemical indicators and AF traits were analyzed. Then, multiple linear regression models were constructed to select the best model used for selecting against AF content. and the heritabilities of plasma indicators contained in the best models were estimated. The results showed that 11 plasma biochemical indicators (triglycerides, total bile acid, total protein, globulin, albumin/globulin, aspartate transaminase, alanine transaminase, gamma-glutamyl transpeptidase, uric acid, creatinine, and VLDL) differed significantly between the lean and fat lines (P linear regression models based on albumin/globulin, VLDL, triglycerides, globulin, total bile acid, and uric acid, had higher R2 (0.73) than the model based only on VLDL (0.21). The plasma parameters included in the best models had moderate heritability estimates (0.21 ≤ h2 ≤ 0.43). These results indicate that these multiple linear regression models can be used to select for lean broiler chickens. © 2017 Poultry Science Association Inc.
Wei, J [City College of New York, New York, NY (United States); Chao, M [The Mount Sinai Medical Center, New York, NY (United States)
2016-06-15
Purpose: To develop a novel strategy to extract the respiratory motion of the thoracic diaphragm from kilovoltage cone beam computed tomography (CBCT) projections by a constrained linear regression optimization technique. Methods: A parabolic function was identified as the geometric model and was employed to fit the shape of the diaphragm on the CBCT projections. The search was initialized by five manually placed seeds on a pre-selected projection image. Temporal redundancies, the enabling phenomenology in video compression and encoding techniques, inherent in the dynamic properties of the diaphragm motion together with the geometrical shape of the diaphragm boundary and the associated algebraic constraint that significantly reduced the searching space of viable parabolic parameters was integrated, which can be effectively optimized by a constrained linear regression approach on the subsequent projections. The innovative algebraic constraints stipulating the kinetic range of the motion and the spatial constraint preventing any unphysical deviations was able to obtain the optimal contour of the diaphragm with minimal initialization. The algorithm was assessed by a fluoroscopic movie acquired at anteriorposterior fixed direction and kilovoltage CBCT projection image sets from four lung and two liver patients. The automatic tracing by the proposed algorithm and manual tracking by a human operator were compared in both space and frequency domains. Results: The error between the estimated and manual detections for the fluoroscopic movie was 0.54mm with standard deviation (SD) of 0.45mm, while the average error for the CBCT projections was 0.79mm with SD of 0.64mm for all enrolled patients. The submillimeter accuracy outcome exhibits the promise of the proposed constrained linear regression approach to track the diaphragm motion on rotational projection images. Conclusion: The new algorithm will provide a potential solution to rendering diaphragm motion and ultimately
Wei, J; Chao, M
2016-01-01
Purpose: To develop a novel strategy to extract the respiratory motion of the thoracic diaphragm from kilovoltage cone beam computed tomography (CBCT) projections by a constrained linear regression optimization technique. Methods: A parabolic function was identified as the geometric model and was employed to fit the shape of the diaphragm on the CBCT projections. The search was initialized by five manually placed seeds on a pre-selected projection image. Temporal redundancies, the enabling phenomenology in video compression and encoding techniques, inherent in the dynamic properties of the diaphragm motion together with the geometrical shape of the diaphragm boundary and the associated algebraic constraint that significantly reduced the searching space of viable parabolic parameters was integrated, which can be effectively optimized by a constrained linear regression approach on the subsequent projections. The innovative algebraic constraints stipulating the kinetic range of the motion and the spatial constraint preventing any unphysical deviations was able to obtain the optimal contour of the diaphragm with minimal initialization. The algorithm was assessed by a fluoroscopic movie acquired at anteriorposterior fixed direction and kilovoltage CBCT projection image sets from four lung and two liver patients. The automatic tracing by the proposed algorithm and manual tracking by a human operator were compared in both space and frequency domains. Results: The error between the estimated and manual detections for the fluoroscopic movie was 0.54mm with standard deviation (SD) of 0.45mm, while the average error for the CBCT projections was 0.79mm with SD of 0.64mm for all enrolled patients. The submillimeter accuracy outcome exhibits the promise of the proposed constrained linear regression approach to track the diaphragm motion on rotational projection images. Conclusion: The new algorithm will provide a potential solution to rendering diaphragm motion and ultimately
Kobrin, Jennifer L.; Sinharay, Sandip; Haberman, Shelby J.; Chajewski, Michael
2011-01-01
This study examined the adequacy of a multiple linear regression model for predicting first-year college grade point average (FYGPA) using SAT[R] scores and high school grade point average (HSGPA). A variety of techniques, both graphical and statistical, were used to examine if it is possible to improve on the linear regression model. The results…
2017-10-01
ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID PROPELLANT GRAIN GEOMETRIES Brian...distribution is unlimited. AD U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER Munitions Engineering Technology Center Picatinny...U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID
Oguntunde, Philip G.; Lischeid, Gunnar; Dietrich, Ottfried
2018-03-01
This study examines the variations of climate variables and rice yield and quantifies the relationships among them using multiple linear regression, principal component analysis, and support vector machine (SVM) analysis in southwest Nigeria. The climate and yield data used was for a period of 36 years between 1980 and 2015. Similar to the observed decrease ( P 1 and explained 83.1% of the total variance of predictor variables. The SVM regression function using the scores of the first principal component explained about 75% of the variance in rice yield data and linear regression about 64%. SVM regression between annual solar radiation values and yield explained 67% of the variance. Only the first component of the principal component analysis (PCA) exhibited a clear long-term trend and sometimes short-term variance similar to that of rice yield. Short-term fluctuations of the scores of the PC1 are closely coupled to those of rice yield during the 1986-1993 and the 2006-2013 periods thereby revealing the inter-annual sensitivity of rice production to climate variability. Solar radiation stands out as the climate variable of highest influence on rice yield, and the influence was especially strong during monsoon and post-monsoon periods, which correspond to the vegetative, booting, flowering, and grain filling stages in the study area. The outcome is expected to provide more in-depth regional-specific climate-rice linkage for screening of better cultivars that can positively respond to future climate fluctuations as well as providing information that may help optimized planting dates for improved radiation use efficiency in the study area.
Oguntunde, Philip G; Lischeid, Gunnar; Dietrich, Ottfried
2018-03-01
This study examines the variations of climate variables and rice yield and quantifies the relationships among them using multiple linear regression, principal component analysis, and support vector machine (SVM) analysis in southwest Nigeria. The climate and yield data used was for a period of 36 years between 1980 and 2015. Similar to the observed decrease (P 1 and explained 83.1% of the total variance of predictor variables. The SVM regression function using the scores of the first principal component explained about 75% of the variance in rice yield data and linear regression about 64%. SVM regression between annual solar radiation values and yield explained 67% of the variance. Only the first component of the principal component analysis (PCA) exhibited a clear long-term trend and sometimes short-term variance similar to that of rice yield. Short-term fluctuations of the scores of the PC1 are closely coupled to those of rice yield during the 1986-1993 and the 2006-2013 periods thereby revealing the inter-annual sensitivity of rice production to climate variability. Solar radiation stands out as the climate variable of highest influence on rice yield, and the influence was especially strong during monsoon and post-monsoon periods, which correspond to the vegetative, booting, flowering, and grain filling stages in the study area. The outcome is expected to provide more in-depth regional-specific climate-rice linkage for screening of better cultivars that can positively respond to future climate fluctuations as well as providing information that may help optimized planting dates for improved radiation use efficiency in the study area.
Lo, Ching F.
1999-01-01
The integration of Radial Basis Function Networks and Back Propagation Neural Networks with the Multiple Linear Regression has been accomplished to map nonlinear response surfaces over a wide range of independent variables in the process of the Modem Design of Experiments. The integrated method is capable to estimate the precision intervals including confidence and predicted intervals. The power of the innovative method has been demonstrated by applying to a set of wind tunnel test data in construction of response surface and estimation of precision interval.
Barrett, C. A.
1985-01-01
Multiple linear regression analysis was used to determine an equation for estimating hot corrosion attack for a series of Ni base cast turbine alloys. The U transform (i.e., 1/sin (% A/100) to the 1/2) was shown to give the best estimate of the dependent variable, y. A complete second degree equation is described for the centered" weight chemistries for the elements Cr, Al, Ti, Mo, W, Cb, Ta, and Co. In addition linear terms for the minor elements C, B, and Zr were added for a basic 47 term equation. The best reduced equation was determined by the stepwise selection method with essentially 13 terms. The Cr term was found to be the most important accounting for 60 percent of the explained variability hot corrosion attack.
Hassan, A K
2015-01-01
In this work, O/W emulsion sets were prepared by using different concentrations of two nonionic surfactants. The two surfactants, tween 80(HLB=15.0) and span 80(HLB=4.3) were used in a fixed proportions equal to 0.55:0.45 respectively. HLB value of the surfactants blends were fixed at 10.185. The surfactants blend concentration is starting from 3% up to 19%. For each O/W emulsion set the conductivity was measured at room temperature (25±2°), 40, 50, 60, 70 and 80°. Applying the simple linear regression least squares method statistical analysis to the temperature-conductivity obtained data determines the effective surfactants blend concentration required for preparing the most stable O/W emulsion. These results were confirmed by applying the physical stability centrifugation testing and the phase inversion temperature range measurements. The results indicated that, the relation which represents the most stable O/W emulsion has the strongest direct linear relationship between temperature and conductivity. This relationship is linear up to 80°. This work proves that, the most stable O/W emulsion is determined via the determination of the maximum R² value by applying of the simple linear regression least squares method to the temperature-conductivity obtained data up to 80°, in addition to, the true maximum slope is represented by the equation which has the maximum R² value. Because the conditions would be changed in a more complex formulation, the method of the determination of the effective surfactants blend concentration was verified by applying it for more complex formulations of 2% O/W miconazole nitrate cream and the results indicate its reproducibility.
Fisz, Jacek J
2006-12-07
The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear
Fiorenza, Alberto; Vincenzi, Giovanni
2011-01-01
Research highlights: → We prove a result true for all linear homogeneous recurrences with constant coefficients. → As a corollary of our results we immediately get the celebrated Poincare' theorem. → The limit of the ratio of adjacent terms is characterized as the unique leading root of the characteristic polynomial. → The Golden Ratio, Kepler limit of the classical Fibonacci sequence, is the unique leading root. → The Kepler limit may differ from the unique root of maximum modulus and multiplicity. - Abstract: For complex linear homogeneous recursive sequences with constant coefficients we find a necessary and sufficient condition for the existence of the limit of the ratio of consecutive terms. The result can be applied even if the characteristic polynomial has not necessarily roots with modulus pairwise distinct, as in the celebrated Poincare's theorem. In case of existence, we characterize the limit as a particular root of the characteristic polynomial, which depends on the initial conditions and that is not necessarily the unique root with maximum modulus and multiplicity. The result extends to a quite general context the way used to find the Golden mean as limit of ratio of consecutive terms of the classical Fibonacci sequence.
Naoki Yamamoto
2011-01-01
Full Text Available A new technique for measuring Young's modulus of an ultra-thin film, with a thickness in the range of about 10 nm, was developed by combining an optical lever technique for measuring the residual stress and X-ray diffraction for measuring the strain in the film. The new technique was applied to analyze the mechanical properties of Ga-doped ZnO (GZO films, that have become the focus of significant attention as a substitute material for indium-tin-oxide transparent electrodes. Young's modulus of the as-deposited GZO films decreased with thickness; the values for 30 nm and 500 nm thick films were 205 GPa and 117 GPa, respectively. The coefficient of linear thermal expansion of the GZO films was measured using the new technique in combination with in-situ residual stress measurement during heat-cycle testing. GZO films with 30–100 nm thickness had a coefficient of linear thermal expansion in the range of 4.3 × 10−6 – 5.6 × 10−6 °C−1.
Kompan, T. A.; Korenev, A. S.; Lukin, A. Ya.
2008-10-01
The artificial material sitall CO-115M was developed purposely as a material with an extra-low thermal expansion. The controlled crystallization of an aluminosilicate glass melt leads to the formation of a mixture of β-spodumen, β-eucryptite, and β-silica anisotropic microcrystals in a matrix of residual glass. Due to the small size of the microcrystals, the material is homogeneous and transparent. Specific lattice anharmonism of these microcrystal materials results in close to zero average thermal linear expansion coefficient (TLEC) of the sitall material. The thermal expansion coefficient of this material was measured using an interferometric method in line with the classical approach of Fizeau. To obtain the highest accuracy, the registration of light intensity of the total interference field was used. Then, the parameters of the interference pattern were calculated. Due to the large amount of information in the interference pattern, the error of the calculated fringe position was less than the size of a pixel of the optical registration system. The thermal expansion coefficient of the sitall CO-115M and its temperature dependence were measured. The TLEC value of about 3 × 10-8 K-1 to 5 × 10-8 K-1 in the temperature interval from -20 °C to +60 °C was obtained. A special investigation was carried out to show the homogeneity of the material.
Chilenski, M.A.; Greenwald, M.; Howard, N.T.; White, A.E.; Rice, J.E.; Walk, J.R.; Marzouk, Y.
2015-01-01
The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, but the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We show that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. We also discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts. (paper)
Jaime-Pérez, José Carlos; Jiménez-Castillo, Raúl Alberto; Vázquez-Hernández, Karina Elizabeth; Salazar-Riojas, Rosario; Méndez-Ramírez, Nereida; Gómez-Almaguer, David
2017-10-01
Advances in automated cell separators have improved the efficiency of plateletpheresis and the possibility of obtaining double products (DP). We assessed cell processor accuracy of predicted platelet (PLT) yields with the goal of a better prediction of DP collections. This retrospective proof-of-concept study included 302 plateletpheresis procedures performed on a Trima Accel v6.0 at the apheresis unit of a hematology department. Donor variables, software predicted yield and actual PLT yield were statistically evaluated. Software prediction was optimized by linear regression analysis and its optimal cut-off to obtain a DP assessed by receiver operating characteristic curve (ROC) modeling. Three hundred and two plateletpheresis procedures were performed; in 271 (89.7%) occasions, donors were men and in 31 (10.3%) women. Pre-donation PLT count had the best direct correlation with actual PLT yield (r = 0.486. P Simple correction derived from linear regression analysis accurately corrected this underestimation and ROC analysis identified a precise cut-off to reliably predict a DP. © 2016 Wiley Periodicals, Inc.
Smith, Timothy D.; Steffen, Christopher J., Jr.; Yungster, Shaye; Keller, Dennis J.
1998-01-01
The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.
Miozzo, Michele; Pulvermüller, Friedemann; Hauk, Olaf
2015-10-01
The time course of brain activation during word production has become an area of increasingly intense investigation in cognitive neuroscience. The predominant view has been that semantic and phonological processes are activated sequentially, at about 150 and 200-400 ms after picture onset. Although evidence from prior studies has been interpreted as supporting this view, these studies were arguably not ideally suited to detect early brain activation of semantic and phonological processes. We here used a multiple linear regression approach to magnetoencephalography (MEG) analysis of picture naming in order to investigate early effects of variables specifically related to visual, semantic, and phonological processing. This was combined with distributed minimum-norm source estimation and region-of-interest analysis. Brain activation associated with visual image complexity appeared in occipital cortex at about 100 ms after picture presentation onset. At about 150 ms, semantic variables became physiologically manifest in left frontotemporal regions. In the same latency range, we found an effect of phonological variables in the left middle temporal gyrus. Our results demonstrate that multiple linear regression analysis is sensitive to early effects of multiple psycholinguistic variables in picture naming. Crucially, our results suggest that access to phonological information might begin in parallel with semantic processing around 150 ms after picture onset. © The Author 2014. Published by Oxford University Press.
Ibanez, C. A. G.; Carcellar, B. G., III; Paringit, E. C.; Argamosa, R. J. L.; Faelga, R. A. G.; Posilero, M. A. V.; Zaragosa, G. P.; Dimayacyac, N. A.
2016-06-01
Diameter-at-Breast-Height Estimation is a prerequisite in various allometric equations estimating important forestry indices like stem volume, basal area, biomass and carbon stock. LiDAR Technology has a means of directly obtaining different forest parameters, except DBH, from the behavior and characteristics of point cloud unique in different forest classes. Extensive tree inventory was done on a two-hectare established sample plot in Mt. Makiling, Laguna for a natural growth forest. Coordinates, height, and canopy cover were measured and types of species were identified to compare to LiDAR derivatives. Multiple linear regression was used to get LiDAR-derived DBH by integrating field-derived DBH and 27 LiDAR-derived parameters at 20m, 10m, and 5m grid resolutions. To know the best combination of parameters in DBH Estimation, all possible combinations of parameters were generated and automated using python scripts and additional regression related libraries such as Numpy, Scipy, and Scikit learn were used. The combination that yields the highest r-squared or coefficient of determination and lowest AIC (Akaike's Information Criterion) and BIC (Bayesian Information Criterion) was determined to be the best equation. The equation is at its best using 11 parameters at 10mgrid size and at of 0.604 r-squared, 154.04 AIC and 175.08 BIC. Combination of parameters may differ among forest classes for further studies. Additional statistical tests can be supplemented to help determine the correlation among parameters such as Kaiser- Meyer-Olkin (KMO) Coefficient and the Barlett's Test for Spherecity (BTS).
Jahandideh, Sepideh; Jahandideh, Samad; Asadabadi, Ebrahim Barzegari; Askarian, Mehrdad; Movahedi, Mohammad Mehdi; Hosseini, Somayyeh; Jahandideh, Mina
2009-01-01
Prediction of the amount of hospital waste production will be helpful in the storage, transportation and disposal of hospital waste management. Based on this fact, two predictor models including artificial neural networks (ANNs) and multiple linear regression (MLR) were applied to predict the rate of medical waste generation totally and in different types of sharp, infectious and general. In this study, a 5-fold cross-validation procedure on a database containing total of 50 hospitals of Fars province (Iran) were used to verify the performance of the models. Three performance measures including MAR, RMSE and R 2 were used to evaluate performance of models. The MLR as a conventional model obtained poor prediction performance measure values. However, MLR distinguished hospital capacity and bed occupancy as more significant parameters. On the other hand, ANNs as a more powerful model, which has not been introduced in predicting rate of medical waste generation, showed high performance measure values, especially 0.99 value of R 2 confirming the good fit of the data. Such satisfactory results could be attributed to the non-linear nature of ANNs in problem solving which provides the opportunity for relating independent variables to dependent ones non-linearly. In conclusion, the obtained results showed that our ANN-based model approach is very promising and may play a useful role in developing a better cost-effective strategy for waste management in future.
Ulf-Peter Hansen
2007-10-01
Full Text Available The demonstrated modified spectrophotometric method makes use of the 2,2-diphenyl-1-picrylhydrazyl (DPPH radical and its specific absorbance properties. Theabsorbance decreases when the radical is reduced by antioxidants. In contrast to otherinvestigations, the absorbance was measured at a wavelength of 550 nm. This wavelengthenabled the measurements of the stable free DPPH radical without interference frommicroalgal pigments. This approach was applied to methanolic microalgae extracts for twodifferent DPPH concentrations. The changes in absorbance measured vs. the concentrationof the methanolic extract resulted in curves with a linear decrease ending in a saturationregion. Linear regression analysis of the linear part of DPPH reduction versus extractconcentration enabled the determination of the microalgaeÃ¢Â€Â™s methanolic extractsantioxidative potentials which was independent to the employed DPPH concentrations. Theresulting slopes showed significant differences (6 - 34 ÃŽÂ¼mol DPPH g-1 extractconcentration between the single different species of microalgae (Anabaena sp.,Isochrysis galbana, Phaeodactylum tricornutum, Porphyridium purpureum, Synechocystissp. PCC6803 in their ability to reduce the DPPH radical. The independency of the signal on the DPPH concentration is a valuable advantage over the determination of the EC50 value.
Brown, A M
2001-06-01
The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.
Robust Multiple Linear Regression.
1982-12-01
difficulty, but it might have more solutions corresponding to local minima. Influence Function of M-Estimates The influence function describes the effect...distributionn n function. In case of M-Estimates the influence function was found to be pro- portional to and given as T(X F)) " C(xpF,T) = .(X.T(F) F(dx...where the inverse of any distribution function F is defined in the usual way as F- (s) = inf{x IF(x) > s) 0<sə Influence Function of L-Estimates In a
Abstract. The predictive analysis based on quantitative structure activity relationships (QSAR) on benzim- ... could lead to treatment of obesity, diabetes and related conditions. ..... After discussing the physical and chemical mean- ing of the ...
(Non) linear regression modelling
Cizek, P.; Gentle, J.E.; Hardle, W.K.; Mori, Y.
2012-01-01
We will study causal relationships of a known form between random variables. Given a model, we distinguish one or more dependent (endogenous) variables Y = (Y1,…,Yl), l ∈ N, which are explained by a model, and independent (exogenous, explanatory) variables X = (X1,…,Xp),p ∈ N, which explain or
Radosavljević Dragana B.
2017-01-01
Full Text Available This paper presents kinetics modeling of essential oil hydrodistillation from juniper berries (Juniperus communis L. by using a non-linear regression methodology. The proposed model has the polynomial-logarithmic form. The initial equation of the proposed non-linear model is q = q∞•(a•(logt2 + b•logt + c and by substituting a1=q∞•a, b1 = q∞•b and c1 = q∞•c, the final equation is obtained as q = a1•(logt2 + b1•logt + c1. In this equation q is the quantity of the obtained oil at time t, while a1, b1 and c1 are parameters to be determined for each sample. From the final equation it can be seen that the key parameter q∞, which presents the maximal oil quantity obtained after infinite time, is already included in parameters a1, b1 and c1. In this way, experimental determination of this parameter is avoided. Using the proposed model with parameters obtained by regression, the values of oil hydrodistillation in time are calculated for each sample and compared to the experimental values. In addition, two kinetic models previously proposed in literature were applied to the same experimental results. The developed model provided better agreements with the experimental values than the two, generally accepted kinetic models of this process. The average values of error measures (RSS, RSE, AIC and MRPD obtained for our model (0.005; 0.017; –84.33; 1.65 were generally lower than the corresponding values of the other two models (0.025; 0.041; –53.20; 3.89 and (0.0035; 0.015; –86.83; 1.59. Also, parameter estimation for the proposed model was significantly simpler (maximum 2 iterations per sample using the non-linear regression than that for the existing models (maximum 9 iterations per sample. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR-35026
Kim, Yong-il; Kim, Yong Joong; Paeng, Jin Chul; Cheon, Gi Jeong; Lee, Dong Soo; Chung, June-Key; Kang, Keon Wook
2017-01-01
18 F-Fluorodeoxyglucose (FDG) positron emission tomography (PET)/computed tomography (CT) has been investigated as a method to predict pancreatic cancer recurrence after pancreatic surgery. We evaluated the recently introduced heterogeneity indices of 18 F-FDG PET/CT used for predicting pancreatic cancer recurrence after surgery and compared them with current clinicopathologic and 18 F-FDG PET/CT parameters. A total of 93 pancreatic ductal adenocarcinoma patients (M:F = 60:33, mean age = 64.2 ± 9.1 years) who underwent preoperative 18 F-FDG PET/CT following pancreatic surgery were retrospectively enrolled. The standardized uptake values (SUVs) and tumor-to-background ratios (TBR) were measured on each 18 F-FDG PET/CT, as metabolic parameters. Metabolic tumor volume (MTV) and total lesion glycolysis (TLG) were examined as volumetric parameters. The coefficient of variance (heterogeneity index-1; SUVmean divided by the standard deviation) and linear regression slopes (heterogeneity index-2) of the MTV, according to SUV thresholds of 2.0, 2.5 and 3.0, were evaluated as heterogeneity indices. Predictive values of clinicopathologic and 18 F-FDG PET/CT parameters and heterogeneity indices were compared in terms of pancreatic cancer recurrence. Seventy patients (75.3%) showed recurrence after pancreatic cancer surgery (mean recurrence = 9.4 ± 8.4 months). Comparing the recurrence and no recurrence patients, all of the 18 F-FDG PET/CT parameters and heterogeneity indices demonstrated significant differences. In univariate Cox-regression analyses, MTV (P = 0.013), TLG (P = 0.007), and heterogeneity index-2 (P = 0.027) were significant. Among the clinicopathologic parameters, CA19-9 (P = 0.025) and venous invasion (P = 0.002) were selected as significant parameters. In multivariate Cox-regression analyses, MTV (P = 0.005), TLG (P = 0.004), and heterogeneity index-2 (P = 0.016) with venous invasion (P < 0.001, 0.001, and 0.001, respectively) demonstrated significant results
Lesnaya, M.I.; Volokitin, G.G.; Kashchuk, V.A.
1976-01-01
Results are reported of an experimental research into the influence of small additions of α-transition metals on the temperature coefficient of linear expansion of titanium and vanadium. Using the configuration model of substance as the basis, expeained are the lowering of the critical liquefaction temperature or the melting point of vanadium and the raising of it, as caused by the addition of metals of the 6 group of the periodic chart and by the addition of metals of the 8 group, respectively, and also a shift in the temperature of the polymorphic α-β-transformation of titanium. Suggested as the best alloying metal for vanadium are tungsten and tantalum; for titaniums is vanadium whose admixtures lower the melting point and shift the polymorphic transformation temperature by as much as 100 to 120 degrees
Tarek Hassan Mohamed
2015-12-01
Full Text Available This paper presented both the linear quadratic Gaussian technique (LQG and the coefficient diagram method (CDM as load frequency controllers in a multi-area power system to deal with the problem of variations in system parameters and load demand change. The full states of the system including the area frequency deviation have been estimated using the Kalman filter technique. The efficiency of the proposed control method has been checked using a digital simulation. Simulation results indicated that, with the proposed CDM + LQG technique, the system is robust in the face of parameter uncertainties and load disturbances. A comparison between the proposed technique and other schemes is carried out, confirming the superiority of the proposed CDM + LQG technique.
Ghaedi, M; Rahimi, Mahmoud Reza; Ghaedi, A M; Tyagi, Inderjeet; Agarwal, Shilpi; Gupta, Vinod Kumar
2016-01-01
Two novel and eco friendly adsorbents namely tin oxide nanoparticles loaded on activated carbon (SnO2-NP-AC) and activated carbon prepared from wood tree Pistacia atlantica (AC-PAW) were used for the rapid removal and fast adsorption of methyl orange (MO) from the aqueous phase. The dependency of MO removal with various adsorption influential parameters was well modeled and optimized using multiple linear regressions (MLR) and least squares support vector regression (LSSVR). The optimal parameters for the LSSVR model were found based on γ value of 0.76 and σ(2) of 0.15. For testing the data set, the mean square error (MSE) values of 0.0010 and the coefficient of determination (R(2)) values of 0.976 were obtained for LSSVR model, and the MSE value of 0.0037 and the R(2) value of 0.897 were obtained for the MLR model. The adsorption equilibrium and kinetic data was found to be well fitted and in good agreement with Langmuir isotherm model and second-order equation and intra-particle diffusion models respectively. The small amount of the proposed SnO2-NP-AC and AC-PAW (0.015 g and 0.08 g) is applicable for successful rapid removal of methyl orange (>95%). The maximum adsorption capacity for SnO2-NP-AC and AC-PAW was 250 mg g(-1) and 125 mg g(-1) respectively. Copyright © 2015 Elsevier Inc. All rights reserved.
Monzavi A
2002-07-01
Full Text Available Waxes have a lot of applications in dentistry. Such materials are of thermoplastic type that undergoes deformation in different temperatures. Two important properties of base plate waxes are flow and their coefficient of linear thermal expansion. Recently, different institutions, inside the country, produce dentistry waxes, while they have not been standardized. Consequently, consumers' dissatisfaction are observed. In this research, the two above- mentioned factors were compared between three kinds of Iranian waxes with Cavex that is foreign production, based on test number 24 of ADA. To measure the flow rate in the temperatures of 23, 37 and 45°c, Wilcoxon statistical analysis was used. The results showed that in 23°c, the flow rate of Cavex and Azardent waxes met ADA standards; however, it was not true for two others types. In 37°c, the flow of none of the waxes was standardized and in 45°c their flow was acceptable, moreover, thermal expansion coefficient, for Cavex and Azardent types, was based on ADA standard.
Dalian Marius DORAN
2017-11-01
Full Text Available The article aims to research impact of budget balance, whether surplus or deficit, on the main indicator characterizing the economic growth of a country, namely GDP and the inflation rate in the 27 European Union Member States and the United Kingdom. For this analysis was used panel data, taking into account the period from 2001 to 2015. The method used for the analysis is the linear regression with fixed effects and with Driscoll-Kraay standard errors. The dependent variables are the growth rate of real GDP and the inflation rate, and the independent variable is the budget balance (surplus or deficit. The results obtained after using econometric software Stata shows a positive impact of budget balance on growth in the European Union for the analyzed period.