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.