Applied Regression Modeling, 2nd Edition

Acknowledgments xvii

Introduction xvii

1.1   Statistics in practice xvii

1.2   Learning statistics xix

1. Foundations 1

1.1 Identifying and summarizing data 1

1.2 Population distributions 5

1.3 Selecting individuals at random—probability 9

1.4 Random sampling 11

1.5 Interval estimation 15

1.6 Hypothesis testing 19

1.7 Random errors and prediction 25

1.8 Chapter summary 28

Problems 29

2. Simple linear regression 35

2.1 Probability model for X and Y 35

2.2 Least squares criterion 40

2.3 Model evaluation 45

2.4 Model assumptions 59

2.5 Model interpretation 66

2.6 Estimation and prediction 68

2.7 Chapter summary 72

Problems 78

3. Multiple linear regression 83

3.1 Probability model for (X₁; X₂; : : : ) and Y 83

3.2 Least squares criterion 87

3.3 Model evaluation 92

3.4 Model assumptions 118

3.5 Model interpretation 124

3.6 Estimation and prediction 126

3.7 Chapter summary 130

Problems 132

4. Regression model building I 137

4.1 Transformations 138

4.2 Interactions 159

4.3 Qualitative predictors 166

4.4 Chapter summary 182

Problems 184

5. Regression model building II 189

5.1 Influential points 189

5.2 Regression pitfalls 199

5.3 Model building guidelines 218

5.4 Model selection 221

5.5 Model interpretation using graphics 224

5.6 Chapter summary 231

Problems 234

6. Case studies 243

6.1 Home prices 243

6.2 Vehicle fuel efficiency 253

6.3 Pharmaceutical patches 261

7. Extensions 267

7.1 Generalized linear models 268

7.2 Discrete choice models 275

7.3 Multilevel models 278

7.4 Bayesian modeling 280

Appendix A. Computer software help 285

Appendix B. Critical values for t distributions 289

Appendix C. Notation and formulas 293

Appendix D. Mathematics refresher 297

Appendix E. Answers to selected problems 299

References 309

Glossary 315

Index 321