Starting with the basic linear model where the design and covariance matrices are of full rank, this book demonstrates how the same statistical ideas can be used to explore the more general linear model with rank-deficient design and/or covariance matrices. The unified treatment presented here provides a clearer understanding of the general linear model from a statistical perspective, thus avoiding the complex matrix-algebraic arguments that are often used in the rank-deficient case. Elegant geometric arguments are used as needed.The book has a very broad coverage, from illustrative practical examples in Regression and Analysis of Variance alongside their implementation using R, to providing comprehensive theory of the general linear model with 181 worked-out examples, 227 exercises with solutions, 152 exercises without solutions (so that they may be used as assignments in a course), and 320 up-to-date references.This completely updated and new edition of Linear Models: An Integrated Approach includes the following features:

Starting with the basic linear model where the design and covariance matrices are of full rank, this book demonstrates how the same statistical ideas can be used to explore the more general linear model with rank-deficient design and/or covariance matrices. The unified treatment presented here provides a clearer understanding of the general linear model from a statistical perspective, thus avoiding the complex matrix-algebraic arguments that are often used in the rank-deficient case. Elegant geometric arguments are used as needed.The book has a very broad coverage, from illustrative practical examples in Regression and Analysis of Variance alongside their implementation using R, to providing comprehensive theory of the general linear model with 181 worked-out examples, 227 exercises with solutions, 152 exercises without solutions (so that they may be used as assignments in a course), and 320 up-to-date references.This completely updated and new edition of Linear Models: An Integrated Approach includes the following features:

Linear Models: An Integrated Approach aims to provide a clear and deep understanding of the general linear model using simple statistical ideas. Elegant geometric arguments are also invoked as needed and a review of vector spaces and matrices is provided to make the treatment self-contained. Complex, matrix-algebraic methods, such as those used in the rank-deficient case, are replaced by statistical proofs that are more transparent and that show the parallels with the simple linear model.

This book has the following special features:
Use of simple statistical ideas such as linear zero functions and covariance adjustment to explain the fundamental as well as advanced concepts
Emphasis on the statistical interpretation of complex algebraic results
A thorough treatment of the singular linear model, including the case of multivariate response
A unified discussion on models with a partially unknown dispersion matrix, including mixed-
effects/variance-components models and models for spatial and time series data
Insight into updates on the linear model and their connection with diagnostics, design, variable
selection, the Kalman filter, etc.
An extensive discussion on the foundations of linear inference, along with linear alternatives to
least squares
Coverage of other special topics, such as collinearity, stochastic and inequality constraints,
misspecified models, etc.
Simpler proofs of numerous known results
Pointers to current research through examples and exercises