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Full Description
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.
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 Selection
12. Heteroscedasticity and Non-independence
13. Models for Binary, Nominal, and Ordinal Response Variables
14. Models for Poisson and Negative Binomial Response
15. Censored Data Models
16. Outliers, Identification, Problems, and Remedies (Good and Bad)
17. Neural Network Regression
18. Regression Trees
19. Bookend
