Linear Regression: Models, Analysis and Applications

Vera L. Beck (Editor)

Series: Mathematics Research Developments, Analytical Chemistry and Microchemistry
BISAC: MAT002050

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Volume 10

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Volume 2

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Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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Chapter One addresses the importance of weighted linear regression in fitting straight lines. In Chapter Two, the authors cover the homocedastic condition, i.e. variance of y’s independent of x, errors of y’s accumulative, the heterocedastic case, i.e. variance or standard deviation proportional to x values, respectively, and orthogonal regression (error in both axes). The chapter also covers topics such as prediction (using the regression line in reverse), leverage, goodness of fit, comparison between models with and without intercept, uncertainty, polynomial regression models without intercept, and an overview of robust regression through the origin. Chapter Three focuses on linear regression for interval-valued data within the framework of random sets, and proposes a new model that generalizes a series of existing ones. Chapter Four provides an investigation on modeling of adsorption of heavy metal ions onto surface-functionalized polymer beads. Linear and non-linear regressions were employed for each of the isotherm models considered to describe the equilibrium data. To reliably assess model validity, various error functions (whose mathematical expressions contain the number of experimental measurements, the numbers of independent variables and parameters in the regression equation as well as the measured and predicted equilibrium adsorption capacities) were used. (Imprint: Nova)

Preface

Chapter 1. Weighting and Transforming Data in Linear Regression
Julia Martín, Alberto Romero Gracia and Agustín G. Asuero (Department of Analytical Chemistry, Faculty of Pharmacy, The University of Seville, Seville, Spain)

Chapter 2. Regression Through the Origin
Julia Martín and Agustín G. Asuero (Department of Analytical Chemistry, Faculty of Pharmacy, The University of Seville, Seville, Spain)

Chapter 3. Linear Regression for Interval-Valued Data in Kc (R)
Yan Sun and Chunyang Li (Department of Mathematics & Statistics, Utah State University, Logan, UT, US)

Chapter 4. Linear Regression versus Non-Linear Regression in Mathematical Modeling of Adsorption Processes
Gabriela-Nicoleta Moroi (Laboratory of Polyaddition and Photochemistry, “Petru Poni” Institute of Macromolecular Chemistry, Iaºi, Romania)

Index

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