Linear Mixed-effects Models Using R by Andrzej Galecki and Tomasz Burzkowski, published by Springer is a book that covers in dept a lot of material on linear models.

The book has clear instructions on how to program in R.

The book in chapter 4 covers model reduction using a null model and alternative model, which are nested models. Model reduction is a topic that needs to be discussed by coders. I have talked with many people who have put everything in a regression model just because they could.

Section 5.2 has the proper form for model formulas

R expression ~ term.1 + term.2 + …+ term.k

It is nice to see this spelled out so clearly.

Chapter 8 shows how to use the nlme package.

Part Three covers Lm’s that allow the relaxing of the assumptions of independence and variance of homogeneity. This a topic that I needed information on.

This is a good reference book.