Understanding Regression Analysis

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 featuresof 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-Xframework is assumed throughout (the fixed-Xcase is presented as a special case of the random-Xcase)
• 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.