Applied Regression Modeling

Preface xv Acknowledgments xix Glossary xxi Introduction xxxi I.1 Statistics in practice xxxi I.2 Learning statistics xxxv 1 Foundations 1 1.1 Identifying and summarizing data 2 1.2 Population distributions 8 1.3 Selecting individuals at random--probability 17 1.4 Random sampling 20 1.4.1 Central limit theorem--normal version 22 1.4.2 Central limit theorem--t-version 25 1.5 Interval estimation 29 1.6 Hypothesis testing 36 1.6.1 The rejection region method 37 1.6.2 The p-value method 42 1.6.3 Hypothesis test errors 49 1.7 Random errors and prediction 50 1.8 Chapter summary 57 Problems 59 2 Simple linear regression 71 2.1 Probability model for and 72 2.2 Least squares criterion 83 2.3 Model evaluation 92 2.3.1 Regression standard error 94 2.3.2 Coefficient of determination--R2 . 98 2.3.3 Slope parameter 107 2.4 Model assumptions 122 2.4.1 Checking the model assumptions 124 2.4.2 Testing the model assumptions 134 2.5 Model interpretation 135 2.6 Estimation and prediction 136 2.6.1 Confidence interval for the population mean, E( ) 137 2.6.2 Prediction interval for an individual -value 141 2.7 Chapter summary 147 2.7.1 Review example 149 Problems 156 3 Multiple linear regression 175 3.1 Probability model for ( 1, 2, ) and 177 3.2 Least squares criterion 184 3.3 Model evaluation 195 3.3.1 Regression standard error 196 3.3.2 Coefficient of determination--R2 . 199 3.3.3 Regression parameters--global usefulness test 214 3.3.4 Regression parameters--nested model test 223 3.3.5 Regression parameters--individual tests 236 3.4 Model assumptions 255 3.4.1 Checking the model assumptions 256 3.4.2 Testing the model assumptions 265 3.5 Model interpretation 270 3.6 Estimation and prediction 273 3.6.1 Confidence interval for the population mean, E( ) 274 3.6.2 Prediction interval for an individual -value 277 3.7 Chapter summary 283 Problems 286 4 Regression model building I 299 4.1 Transformations 302 4.1.1 Natural logarithm transformation for predictors 302 4.1.2 Polynomial transformation for predictors 312 4.1.3 Reciprocal transformation for predictors 321 4.1.4 Natural logarithm transformation for the response 328 4.1.5 Transformations for the response and predictors 336 4.2 Interactions 343 4.3 Qualitative predictors 357 4.3.1 Qualitative predictors with two levels 358 4.3.2 Qualitative predictors with three or more levels 374 4.4 Chapter summary 392 Problems 395 5 Regression model building II 413 5.1 Influential points 416 5.1.1 Outliers 416 5.1.2 Leverage 424 5.1.3 Cook's distance 429 5.2 Regression pitfalls 435 5.2.1 Nonconstant variance 435 5.2.2 Autocorrelation 442 5.2.3 Multicollinearity 450 5.2.4 Excluding important predictor variables 458 5.2.5 Overfitting 463 5.2.6 Extrapolation 465 5.2.7 Missing data 469 5.2.8 Power and sample size 475 5.3 Model building guidelines 478 5.4 Model selection 484 5.5 Model interpretation using graphics 491 5.6 Chapter summary 504 Problems 508 C Notation and formulas 635 C.1 Univariate data 635 C.2 Simple linear regression 637 C.3 Multiple linear regression 639