Graybill F.A. An Introduction to Linear Statistical Models. Vol. I

McGraw-Hill, 1961. – 463 p.This is a well-organized and clearly written text on multiple linear regression including its application to design of experiments, analysis of variance, and the estimation of components of variance. The prerequisites for the student are an introduction to mathematical statistics at about the level of Mood and a good course in matrices. A limitation is that the book concentrates on the mathematical treatment of statistical models. The student is given practically no advice on the construction of models and almost no experience in the analysis of real bodies of data. As the author says, "no attempt is made to justify any model for a given real-world situation." This is a pity. Historically, the theory of multiple regression was developed not for its mathematical beauty, but as a tool for analyzing data. In experience the teaching of the sound application of multiple regression theory to actual data is the hardest part of the course, both for lecturer and students.
To summarize, the book succeeds admirably in what it sets out to do, though that teachers who use it will present a broader view of the subject.