Praise for the Second Edition "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.

Table of Contents:
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