Understanding Regression Analysis

Understanding Regression Analysis 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 from the outset takes a realistic approach 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 chapter-review 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.