Linear Models in Statistics

Alvin C. Rencher, G. Bruce Schaalje0471754986, 9780471754985

Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models.The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed.This modern Second Edition features:*New chapters on Bayesian linear models as well as random and mixed linear models*Expanded discussion of two-way models with empty cells*Additional sections on the geometry of least squares*Updated coverage of simultaneous inferenceThe book is complemented with easy-to-read proofs, real data sets,and an extensive bibliography. A thorough review of the requisite matrix algebra has been added for transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS(r) code for all numerical examples.Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.

---

Table of contents :
Frontmatter……Page 2
1 Introduction……Page 17
2 Matrix Algebra……Page 21
3 Random Vectors and Matrices……Page 85
4 Multivariate Normal Distribution……Page 102
5 Distribution of Quadratic Forms in y……Page 119
6 Simple Linear Regression……Page 140
7 Multiple Regression: Estimation……Page 150
8 Multiple Regression: Tests of Hypotheses and Confidence Intervals……Page 198
9 Multiple Regression: Model Validation and Diagnostics……Page 239
10 Multiple Regression: Random x’s……Page 254
11 Multiple Regression: Bayesian Inference……Page 288
12 Analysis-of-Variance Models……Page 306
13 One-Way Analysis-of-Variance: Balanced Case……Page 350
14 Two-Way Analysis-of-Variance: Balanced Case……Page 387
15 Analysis-of-Variance: The Cell Means Model for Unbalanced Data……Page 423
16 Analysis-of-Covariance……Page 453
17 Linear Mixed Models……Page 488
18 Additional Models……Page 516
Appendix A Answers and Hints to the Problems……Page 526
References……Page 661
Index……Page 670