Norman Richard Draper (1931–2022)

Applied Regression Analysis is, as one might expect, a textbook concerning the methods and application of regression analysis. The book is laid out in the usual fashion: An initial introductory chapter describing the whys and wherefores of linear regression, a second chapter which re-casts the first chapter in terms of matrix algebra, a third chapter on residual analysis and then a series of chapters that branch off into discussing and teaching a variety of regression subjects such as show more multiple predictor variables, “best” regression equation, model building, multiple regression applied to ANOVA, and a final chapter with an introduction to non-linear regression.

For me, as a practicing statistician for many years, what sets this book apart from its counterparts are Chapters 1 and 3. The discussion of the basic concepts of simple linear regression in Chapter 1, particularly the discussion from pages 8 to 31 of the 2nd edition, is simply the best explanation of the process I have encountered. Of particular value are the paragraphs and sentences in section 1.4 – Examining the Regression Equation. I have quoted the words at the bottom of page 22 and the top of page 23 to more people under more circumstances than I can recall. They completely destroy the ridiculous notion offered up in books, papers, internet chat rooms, etc. concerning the supposed need for Y and/or X to be normally distributed before one can use regression analysis to analyze the data.

As for Chapter 3 – it clearly explains the NEED for graphical analysis of residuals. It also, by illustration, provides an understanding of why the current general practice of just applying tests such as the Anderson-Darling or the Shapiro-Wilks or any other test for normality of residuals without a first careful examination of the graphs of the residuals guarantees you will go wrong with great assurance.

About the only major residual pattern not discussed in Chapter 3 is that of sloped parallel lines. For the interested reader, Searle discussed this pattern in a 1988 article in Technometrics.

This copy is the 2nd edition of the book. It has gone into a 3rd edition and is still available. I would recommend this book to anyone interested in learning the methods of linear regression or in obtaining a better understanding of what is going on when you click on “run regression” in whatever statistics package you happen to be using. show less