I am finishing 'Introduction to the Theory of Statistics' (Mood, Graybill, Boes). Now I want to learn how to do statistics but with many variables (matrices). I am considering the following books:

Methods Multivariate Analysis (Rencher) https://www.amazon.com/Methods-Multivariate-Analysis-Alvin-Rencher/dp/0470178965/ref=sr_1_3?s=books&ie=UTF8&qid=1530175623&sr=1-3&keywords=alvin+rencher

Linear Models in Statistics (Rencher) https://www.amazon.com/Linear-Models-Statistics-Alvin-Rencher/dp/0471754986/ref=sr_1_1?ie=UTF8&qid=1530189102&sr=8-1&keywords=linear+models+in+statistics

Which is more logical to be read first? Or should I read something else?

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    $\begingroup$ Neither. Seber and Lee Linear Regression Analysis. $\endgroup$ – AdamO Jun 30 '18 at 3:07
  • $\begingroup$ @AdamO Thank you for your response. Can you please briefly explain why you recommend Seber and Lee's Linear Regression Analysis over these two books? $\endgroup$ – Noppawee Apichonpongpan Jul 1 '18 at 3:44
  • $\begingroup$ I should clarify: Rencher's ToCs are ambitious: they cover pure matrix algebra, and pure probability theory which should be reviewed elsewhere. The Matrix Cookbook is a popular resource. The ToC then covers many popular models: ANOVAs and linear models are covered separately. They are, in fact, equivalent procedures. To dedicate such large sections of a book on multivariate methods (which are mathematically equivalent) seems ironic and to be missing the point. $\endgroup$ – AdamO Jul 2 '18 at 19:56
  • $\begingroup$ Seber and Lee is an academic standard. Their treatment is on the linear model, and presents a general case for t-tests, ordinary least squares, the Gauss Markov theorem, and maximum likelihood. This is the point of learning theory: to understand the concepts and connections from a high level perspective so that application is made easier. The algebra review is pushed to the appendix, and covers some aspects of computational algebra which is undoubtedly important (many CV Q's are just issues of debugging R's INLA and BLAST -linear algebra packages). $\endgroup$ – AdamO Jul 2 '18 at 19:59
  • $\begingroup$ So I should study matrix algebra (from some other book) then study Seber and Lee? $\endgroup$ – Noppawee Apichonpongpan Jul 3 '18 at 3:35

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