Understanding Regression Analysis: A Conditional Distribution Approach, 1st Edition (Hardback) book cover

Understanding Regression Analysis

A Conditional Distribution Approach, 1st Edition

By Peter Westfall, Andrea L. Arias

Chapman and Hall/CRC

480 pages | 173 B/W Illus.

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Hardback: 9780367458522
pub: 2020-06-11
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Description

This book unifies diverse regression applications including the classical model, ANOVA models, generalized models including Poisson, Negative binomial, logistic, and survival, neural networks and decision trees under a common umbrella; namely, the conditional distribution model. It explains why the conditional distribution model is the correct model, and it also explains (proves) why the assumptions of the classical regression model are wrong. Unlike other regression books, this one takes a realistic approach from the outset that all models are just approximations. Hence, the emphasis is to model Nature’s processes realistically, rather than to assume (incorrectly) that Nature works in particular, constrained ways.

Key features of the book include:

  • Numerous worked examples using the R software
  • Key points and self-study questions displayed "just-in-time" within chapters
  • Simple mathematical explanations ("baby proofs") of key concepts
  • Clear explanations and applications of statistical significance (p-values), incorporating the American Statistical Association guidelines
  • Use of "data-generating process" terminology rather than "population"
  • Random-X framework is assumed throughout (the fixed-X case is presented as a special case of the random-X case)
  • Clear explanations of probabilistic modelling, including likelihood-based methods
  • Use of simulations throughout to explain concepts and to perform data analyses

This book has a strong orientation towards science in general, as well as end-of chapter and self-study questions, so it can be used as a textbook for research-oriented students in the social, biological and medical, and physical and engineering sciences. As well, its mathematical emphasis makes it ideal for a text in mathematics and statistics courses. With its numerous worked examples, it is also ideally suited to be a reference book for all scientists.

Table of Contents

1. Introduction to Regression Models

2. Estimating Regression Model Parameters

3. The Classical Model and Its Consequences

4. Evaluating Assumptions

5. Transformations

6. The Multiple Regression Model

7. Multiple Regression from the Matrix Point of View

8. R-squared, Adjusted R-Squared, the F Test, and Multicollinearity

9. Polynomial Models and Interaction (Moderator) Analysis

10. ANOVA, ANCOVA, and Other Applications of Indicator Variables

11. Variable and Model Selection

12. Heteroscedasticity and Non-Independence

13. Models for Binary, Ordinal, and Nominal Response Variables

14. Models for Poisson and Negative Binomial Response

15. Censored Data Models

16. Outliers

17. Neural Network Regression

18. Tree Regression

19. Bookend

About the Authors

Peter H. Westfall has a Ph.D. in Statistics from the University of California at Davis, as well as many years of teaching, research, and consulting experience, in a variety of statistics-related disciplines. He has published over 100 papers on statistical theory, methods, and applications; and he has written several books, spanning academic, practitioner, and textbook genres. He is former editor of The American Statistician, and a Fellow of the American Statistical Association.

Andrea L. Arias is a Senior Operations Research Specialist at BNSF Railway. She has a Ph.D. in Industrial Engineering with a minor in Business Statistics from Texas Tech University, and a Doctoral Degree in Industrial Engineering from Pontificia Universidad Católica de Valparaiso, Chile. Her main areas of expertise include Mathematical Programming, Network Optimization, Statistics and Simulation. She is an active member of the Institute for Operations Research and the Management Sciences (INFORMS.)

Subject Categories

BISAC Subject Codes/Headings:
BUS061000
BUSINESS & ECONOMICS / Statistics
MAT029000
MATHEMATICS / Probability & Statistics / General