This textbook provides a wide-ranging introduction to the use of linear models in analyzing data. The author's emphasis is on providing a unified treatment of the analysis of variance models and regression models by presenting a vector space and projections approach to the subject. Every chapter comes with numerous exercises and examples which will make it ideal for a graduate-level course on this subject. All the standard topics are covered in depth: ANOVA, estimation, hypothesis testing, multiple comparison, regression analysis, experimental design. In addition this book covers topics which are not usually treated at this level, but which are important in their own right: testing for lack of fit, models with singular covariance matrices, variance component estimation, best linear prediction, collinearity, and variable selection. In this new edition, the author has added new examples, and discussions of Bayesian estimation, testing independence assumptions, and interblock analysis.