Methods and Applications of Linear Models (3^rd Ed.)
Regression and the Analysis of Variance
Wiley Series in Probability and Statistics Series

"An essential desktop reference book . . . it should definitely be on your bookshelf."
?Technometrics

A thoroughly updated book, Methods and Applications of Linear Models: Regression and the Analysis of Variance, Third Edition features innovative approaches to understanding and working with models and theory of linear regression. The Third Edition provides readers with the necessary theoretical concepts, which are presented using intuitive ideas rather than complicated proofs, to describe the inference that is appropriate for the methods being discussed.

The book presents a unique discussion that combines coverage of mathematical theory of linear models with analysis of variance models, providing readers with a comprehensive understanding of both the theoretical and technical aspects of linear models. With a new focus on fixed effects models, Methods and Applications of Linear Models: Regression and the Analysis of Variance, Third Edition also features:

• Newly added topics including least squares, the cell means model, and graphical inspection of data in the AVE method
• Frequent conceptual and numerical examples for clarifying the statistical analyses and demonstrating potential pitfalls
• Graphics and computations developed using JMP® software to accompany the concepts and techniques presented
• Numerous exercises presented to test readers and deepen their understanding of the material

An ideal book for courses on linear models and linear regression at the undergraduate and graduate levels, the Third Edition of Methods and Applications of Linear Models: Regression and the Analysis of Variance is also a valuable reference for applied statisticians and researchers who utilize linear model methodology.

Preface to the Third Edition xvii

Preface to the Second Edition xix

Preface to the First Edition xxi

Part I Regression 1

1 Introduction to Linear Models 3

1.1 Background Information 3

1.2 Mathematical and Statistical Models 5

1.3 Definition of the Linear Model 8

1.4 Examples of Regression Models 13

1.5 Concluding Comments 21

Exercises 21

2 Regression on Functions of One Variable 23

2.1 The Simple Linear Regression Model 23

2.2 Parameter Estimation 25

2.3 Properties of the Estimators and Test Statistics 34

2.4 The Analysis of Simple Linear Regression Models 39

2.5 Examining the Data and the Model 50

2.6 Polynomial Regression Models 63

Exercises 72

3 Transforming the Data 81

3.1 The Need for Transformations 81

3.2 Weighted Least Squares 82

3.3 Variance Stabilizing Transformations 85

3.4 Transformations to Achieve a Linear Model 86

3.5 Analysis of the Transformed Model 92

Exercises 95

4 Regression on Functions of Several Variables 99

4.1 The Multiple Linear Regression Model 99

4.2 Preliminary Data Analysis 100

4.3 Analysis of the Multiple Linear Regression Model 103

4.4 Partial Correlation and Added-Variable Plots 113

4.5 Variable Selection 119

4.6 Model Specification 130

Exercises 137

5 Collinearity in Multiple Linear Regression 142

5.1 The Collinearity Problem 142

5.2 An Example with Collinearity 150

5.3 Collinearity Diagnostics 156

5.4 Remedial Solutions: Biased Estimators 1665.4.3 Ridge Regression 174

Exercises 178

6 Influential Observations in Multiple Linear Regression 182

6.1 The Influential Data Problem 182

6.2 The Hat Matrix 183

6.3 The Effects of Deleting Observations 188

6.4 Numerical Measures of Influence 192

6.5 The Dilemma Data 197

6.6 Plots for Identifying Unusual Cases 201

6.7 Robust/Resistant Methods in Regression Analysis 209

Exercises 213

7 Polynomial Models and Qualitative Predictors 216

7.1 Polynomial Models 216

7.2 The Analysis of Response Surfaces 220

7.3 Models with Qualitative Predictors 225

Exercises 247

8 Additional Topics 254

8.1 Nonlinear Regression Models 254

8.2 Nonparametric Model-Fitting Methods 260

8.3 Generalized Linear Models 265

8.4 Random Input Variables 274

8.5 Errors in the Inputs 276

8.6 Calibration 277

Exercises 278

Part II the Analysis of Variance 283

9 Classification Models I: Introduction 285

9.1 Background Information 285

9.2 The One-Way Classification Model 286

9.3 The Two-Way Classification Model: Balanced Data 304

9.4 The Two-Way Classification Model: Unbalanced Data 322

9.5 The Two-Way Classification Model: No Interaction 334

9.6 Concluding Comments 347

Exercises 347

10 The Mathematical Theory of Linear Models 359

10.1 The Distribution of Linear and Quadratic Forms 359

10.2 Estimation and Inference for Linear Models 368

10.3 Tests of Linear Hypotheses on β 380

10.4 Confidence Regions and Intervals 392

Exercises 395

11 Classification Models II: Multiple Crossed and Nested Factors 405

11.1 The Three-Factor Cross-Classified Model 406

11.2 A General Structure for Balanced Factorial Models 412

11.3 The Twofold Nested Model 417

11.4 A General Structure for Balanced, Nested Models 426

11.5 A Three-Factor, Nested-Factorial Model 429

11.6 A General Structure for Balanced, Nested-Factorial Models 434

Exercises 438

12 Mixed Models I: The AOV Method with Balanced Data 443

12.1 Introduction 443

12.2 Examples of the Analysis of Mixed Models 444

12.3 The General Analysis for Balanced, Mixed Models 464

12.4 Additional Examples 479

12.5 Alternative Developments of Mixed Models 487

Exercises 493

13 Mixed Models II: The AVE Method with Balanced Data 499

13.1 Introduction 499

13.2 The Two-Way Cross-Classification Model 500

13.3 The Three-Factor, Cross-Classification Model 511

13.4 Nested Models 515

13.5 Nested-Factorial Models 518

13.6 A General Description of the AVE Table 524

13.7 Additional Examples 531

13.8 The Computational Procedure for the AVE Method 537

Exercises 537

14 Mixed Models III: Unbalanced Data 543

14.1 Introduction 543

14.2 Parameter Estimation: Likelihood Methods 545

14.3 ml and REml Estimates with Balanced Data 554

14.4 The EM Algorithm for REML Estimation 558

14.5 Diagnostic Analysis with the EM Algorithm 572

14.6 Models with Covariates 581

14.7 Summary 585

Exercises 585

15 Simultaneous Inference: Tests and Confidence Intervals 591

15.1 Simultaneous Tests 591

15.2 Simultaneous Confidence Intervals 610

Exercises 612

Appendix A Mathematics 615

Appendix B Statistics 634

Appendix C Data Tables 645

Appendix D Statistical Tables 660

References 669

Index 677

RONALD R. HOCKING, PhD, is Professor Emeritus in the Department of Statistics and Founder of the Ronald R. Hocking Lecture Series at Texas A&M University. A Fellow of the American Statistical Association, Dr. Hocking is the recipient of numerous honors in the statistical community including the Shewell Award, the Youden Award, the Wilcoxon Award, the Snedecor Award, and the Owen Award.