Thoroughly revised and updated with the latest results, this Third Edition provides an account of the theory and applications of linear models. The authors present a unified theory of inference from linear models and its generalizations with minimal assumptions. They not only use least squares theory, but also alternative methods of estimation and testing based on convex loss functions and general estimating equations. Highlights include sensitivity analysis and model selection, an analysis of incomplete data, and an analysis of categorical data based on a unified presentation of generalized linear models. There is also an extensive appendix on matrix theory that is particularly useful for researchers in econometrics, engineering, and optimization theory. This text is recommended for courses in statistics at the graduate level as well as for other courses in which linear models play a role.