Monahan (mathematics, North Carolina State U.) advises starting with the appendix (a review of linear algebra) if readers wish to build their skills from the basic to the more complex, and provides a wealth of proofs and commentary from both algebraic and geometric viewpoints to get them through this unifies and thorough development of the theory behind the statistical methodology of regression and the analysis of variance (ANOVA). Using non-full-rank design matrices and numerous models, Monahan covers the linear least squares problem, estimability and least squares estimators, the Gauss-Markov model, distributional theory, statistical inference, topics in testing (such as orthogonal polynomials and contrasts), variance components and mixed models, and the multivariate linear model. He also provides exercises and a second appendix on Lagrange multipliers along with a well-chosen bibliography. The result is a concise treatment that is comprehensive without being intimidating. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)