A Modern Approach to Regression with R

by Simon J. Sheather

This book focuses on tools and techniques for building regression models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to base inferences or conclusions only on valid models. Plots are shown to be an important tool for both building regression models and assessing their validity. We shall see that deciding what to plot and how each plot should be interpreted will be a major challenge. In order to overcome this challenge we shall need to understand the mathematical properties of the fitted regression models and associated diagnostic procedures. As such this will be an area of focus throughout the book. In particular, we shall carefully study the properties of resi- als in order to understand when patterns in residual plots provide direct information about model misspecification and when they do not. The regression output and plots that appear throughout the book have been gen- ated using R. The output from R that appears in this book has been edited in minor ways. On the book web site you will find the R code used in each example in the text.

Kindle Edition

First published November 19, 2008

Reviews

[Jerzy · Rating 4 out of 5]

I'd like to read the whole thing some time: I've only skimmed it to review the material. But it seems solid, including several helpful ideas I wasn't familiar with.

* p.103 and p.252: some great flowcharts, to make sure you don't miss the key steps, for simple and multiple linear regression
* p.159: residual plots do NOT clearly indicate which part of the model is misspecified; e.g. the plots may look like there's nonconstant variance, but it might actually be that the mean function is badly specified
* p.161: try Sliced Inverse Regression (Li 1991) to determine the number and kinds of transformations required on the various variables if you can't visualize them all at once
* p.166: added-variable plot example: sometimes plotting Y|X(-i) vs Xi|X(-i) shows that some of the Xi are unhelpful once you have the other variables in the model already
* p.176: either try transforming (X1,...,Xp,Y) to joint multivariate normality using multivariate Box-Cox; or try transforming all the X's to joint multivar normality, then fit Yhat from these transformed X's, then use an inverse response plot to choose the transformation for Y, i.e. plot Y vs Yhat to find a good g s.t. g(Y)=Yhat (see p.171)
* p.192: marginal mean plots: scatterplot Y vs Xi, loess Y ~ Xi, and loess Yhat ~ Xi (where Yhat is from full model on all X's), to see whether the full model looks good marginally
* p.238: remember that if you do variable selection first, then your p-values will be underestimates of the true p-values you "should" be getting, i.e. they're biased towards falsely appearing significant: "the sampling properties of post-model-selection estimators are typically significantly different from the nominal distributions that arise if a fixed model is supposed"

[Betsy Rosalen · Rating 3 out of 5]

I wish that the R code was in the book not in a separate book website. I also wish there was more explanation of how to interpret R outputs. This is a common complaint I have iwth many R textbooks though. It's not enough to say, "You can see in the output that..." you need to explain how you see that? What exactly is indicating that conclusion... Also it could use some updating. Some of the R code uses deprecated functions that I had a hard time finding the updated functions for. I also had trouble with some topics like how to use R to determine Box-Cox transformations on predictor variables and how to determine the right weight to use for weighted regression. Maybe it's just because some of the math was beyond my comprehension, but there didn't seem to be an explanation at all let aloe one I couldn't understand.

[Amy · Rating 4 out of 5]

Concise yet comprehensive overview of regression techniques. Some insights were presented without a rigorous background, but the introduction of the material opens the avenue for you to research further about the topic presented.

I found the wording a little convoluted at times, but overall a fairly good introduction to regression approaches. Would recommend supplementing with a course or stats videos online.

[Gerry Scheetz · Rating 4 out of 5]

Used as part of a Data Analytics class
Math was good and easy to follow
R was a little old