I have done a course in Simple Linear Regression and I am aware of linear statistical models (I follow the book by C.R. Rao). Keeping this background in mind, please suggest some good book(s) for multiple regression and multivariate analysis. The book(s) may contain only a well-written comprehensive chapter on this subject : I have no objection to that, though a book written on this only, is preferable. I have no idea about Multiple Regression and Multivariate Analysis, hence it will be great if the book(s) concerned DEVELOPS the subject from the basics and then delves deeper into the theory. A large number of exercises (good quality) is preferred, though not mandatory (if the theory itself is very good). Thanks!!
If you need to choose "only one" book I would go with Applied Linear Statistical Models by Neter, Kutner, Nachtsheim and Wasserman. I never owned it (always someone else in the office did) but it never failed to provide me with the some of the best reference material on the multiple regression.
It started from
Simple Linear Regression proceeded to
Multiple Linear Regression and
Non-linear regression to move onto
Single and then
Multiple Factor Analysis Studies to finish off with
Specialized Design Studies (eg. Latin Squares, Response Surface Methodology, etc.). Take notice this is not a small book; at ~1400 page is one of the largest Stats book I have seen.
(I have noticed the "Applied Linear Regression Models" suggested earlier. I have not seen that book I suspect the cover a lot of common ground so +1 to that!)
As a second choice a "golden oldie" that was (somewhat) recently rewritten is: Linear Regression Analysis by Seber and Lee. It is a bit theoretical and less applied than the Neter et al. book. If more of a theory is your thing it will worth your time. Do not worry it is not full of asymptotics; just it is less "practical" than the Neter et al. book. :)
I liked the book by Seber more because I found it more concise and easier to use if you already have some basis on linear regression. I accept that it might be less friendly to a newcomer though. Given you have already done a course on simple linear regression you will not have a problem I believe (your Linear Algebra is OK right?).
I suggest Methods of Multivariate Analysis by Alvin C. Rencher and William F. Christensen.
Are you asking about a theory book or an applied one?
For an intermediate book on applied linear regression models, I'm in total love with Applied Linear Regression Models (5th edition) by Kutner. It builds from scratch, and it's certainly a comprehensive book on the subject. It explains every theoretical aspect you should know and it teaches you the usual flow of model building, selection, validation, diagnostics and remedial measures.
The only topic it failed to explain is power transformations. While it is treated on several parts of the book, it doesn't have the depth I needed.
I'll insist you should't miss this book. At least, give it a good read at the table of contents to see if it fits your needs.
The first book covers multiple regression in an applied sense very well, while the second is good on multivariate theory, and many skips many of the practical matters that Cohen&Cohen cover.
My personal favourite for beginners is Muirhead (1982). It is much more intuitive and clearer than any other book I have encountered. It covers all bases of MANOVA, ANOVA etc. and the first three chapters will give you the toolkit to understand incredibly deep concepts.
Also there is Anderson's textbook but that is very dense and less useful. Johnson and Kotz is mainly a reference to look things up.
Muirhead is here. Also Clive Granger has a very good reputation for writing textbooks if you're into time series.
Conclusion: go with Muirhead's book. It will make you understand things and is much better suited to beginners.