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Series Editor's Introduction                                      xi

Preface                                                         xvii

1. Prologue: Regression Analysis as Problematic                1
2. A Grounded Introduction to Regression Analysis              5
2.1 Some Examples of Regression Analysis                   5
2.1.1 Abortion and Subsequent Crime                   5
2.1.2 Mandatory Basic Education
for Welfare Recipients                          6
2.1.3 Gender and Academic Salaries                    7
2.1.4  Climate Change and Water Resources in India     8
2.1.5 Deforestation and Soil Erosion in the Yangtze
River Valley                                     8
2.1.6 Epidemics of Hepatitis C                        9
2.1.7 Onward and Upward                               9
2.2 What Is Regression Analysis?                             10
2.2.1 A Simple Illustration                             10
2.2.2 Controlling for a Third Variable                  13
2.2.3 Imposing a Smoother                               16
2.3 Getting From Data to Stories                             18
3. Simple Linear Regression                                      21
3.1 Introduction                                             21
3.2  Describing a Conditional Relationship
With a Straight Line                                    22
3.3 Defining the "Best" Line                                 24
3.4 Some Useful Formulas                                     27
3.5 Standardized Slopes                                      28
3.6 Using Transformations for a Nonlinear Fit                30
3.7 What About the Variance Function?                        35
3.8 Summary and Conclusions                                  37
4. Statistical Inference for Simple Linear Regression         39
4.1 The Role of Sampling                                     39
4.1.1 Random Sampling                                   39
4.1.2  Strategy I: Treating the Data as Population    42

4.1.3  Strategy II: Treating the Data as If They Were
Generated by Random Sampling From a Population  44
4.1.4  Strategy III: Inventing an Imaginary Population  51
4.1.5  Strategy IV: Model-Based Sampling-Inventing
a Friendly Natural Process Responsible for the Data  53
4.1.6 A Note on Randomization Inference                56
4.1.7 Summing Up                                       58
4.2 Simple Linear Regression Under Random Sampling       58
4.2.1  Estimating the Population Regression Line     58
4.2.2 Estimating the Standard Errors                   61
4.2.3  Estimation Under Model-Based Sampling           62
4.2.4 Some Things That Can Go Wrong                    62
4.2.5 Tests and Confidence Intervals                   65
4.3 Statistical Power                                       69
4.4 Stochastic Predictors                                   69
4.5 Measurement Error                                       73
4.6 Can Resampling Techniques Help?                         74
4.6.1 Percentile Confidence Intervals                  76
4.6.2 Hypothesis Testing                               77
4.6.3 Bootstrapping Regression                         77
4.6.4 Possible Benefits From Resampling                78
4.7 Summary and Conclusions                                 79
5. Causal Inference for the Simple Linear Model                 81
5.1 Introduction                                            81
5.2 Some Definitions: What's a Causal Effect?               82
5.2.1 The Neyman-Rubin Model                           84
as Response Schedules                            88
5.2.3 What's an Intervention?                          90
5.3 Studying Cause and Effect With Data                     97
5.3.1  Using Nonstatistical Solutions
for Making Causal Inferences                     97
5.3.2  Using Statistical Solutions for Making
Causal Inferences                                98
5.3.3  Using the Simple Linear Model
for Making Causal Inferences                     99
5.4 Summary and Conclusions                                101
6. The Formalities of Multiple Regression                      103
6.1 Introduction                                           103
6.2 Terms and Predictors                                   103
6.3 Some Notation for Multiple Regression                  105

6.4 Estimation                                              105
6.5 How Multiple Regression "Holds Constant"                107
6.6 Summary and Conclusions                                 110
7. Using and Interpreting Multiple Regression                   111
7.1 Introduction                                            111
7.2 Another Formal Perspective on Holding Constant      111
7.3 When Does Holding Constant Make Sense?                  113
7.4  Standardized Regression Coefficients:
Once More With Feeling                                 117
7.5 Variances of the Coefficient Estimates                  119
7.6 Summary and Conclusions                                 122
8. Some Popular Extensions of Multiple Regression          125
8.1 Introduction                                            125
8.2 Model Selection and Stepwise Regression                 126
8.2.1 Model Selection by Removing Terms                127
8.2.2 Tests to Compare Models                          128
8.2.3 Selecting Terms Without Testing                  130
8.2.4 Stepwise Selection Methods                       132
8.2.5 Some Implications                                133
8.3 Using Categorical Terms: Analysis of Variance
and Analysis of Covariance                             135
8.3.1 An Extended Example                              135
8.4 Back to the Variance Function:
Weighted Least Squares                                 141
8.4.1 Visualizing Lack of Fit                          141
8.4.2  Weighted Least Squares as a Possible Fix    142
8.4.3 Evaluating the Mean Function                     145
8.5 Locally Weighted Regression Smoother                    147
8.6 Summary and Conclusions                                 148
9. Some Regression Diagnostics                                  151
9.1 Introduction                                            151
9.2 Transformations of the Response Variable                152
9.2.1 Box-Cox Procedures                               152
9.2.2 Inverse Fitted Value Response Plots          153
9.3 Leverage and Influence                                  159
9.3.1 Influential Cases and Cook's Distance        159
9.4 Cross-Validation                                        162
9.5 Misspecification Tests                                  163
9.5.1 Instrumental Variables                           164
9.5.2 Tests for Exogeneity                             167
9.6 Conclusions                                             168

10. Further Extensions of Regression Analysis                   171
10.1 Regression Models for Longitudinal Data               171
10.1.1 Multiple Linear Regression for Time Series Data  172
10.2 Regression Analysis With Multiple
Time Series Data                                      177
10.2.1 Fixed Effects Models                           178
10.2.2 Random Effects Models                          178
10.2.3 Estimation                                     180
10.3 Multilevel Models                                     180
10.4 The Generalized Linear Model                          183
10.4.1 GLM Structure                                  183
10.4.2 Normal Models                                  184
10.4.3 Poisson Models                                 184
10.4.4 Poisson Models for Contingency Tables        186
10.4.5 Binomial Regression                            186
10.5 Multiple Equation Models                              188
10.5.1 Causal Inference Once Again                    191
10.5.2 A Final Observation                            196
10.6 Meta-Analysis                                         196
10.7 Conclusions                                           200
11. What to Do                                                  203
11.1 How Did We Get Into This Mess?                        203
11.2 Three Cheers for Description                          206
11.2.1 What's Description?                            207
11.2.3 Descriptive Regressions as Part of a Broad
Research Program                               209
11.2.4 Spotting Provocative Associations              210
11.2.5 Some Other Benefits of Description             212
11.3 Two Cheers for Statistical Inference                  218
11.3.1 Working With Near-Random Samples               220
11.3.2 Working With Data From Nature                  222
11.3.3 Working With a Nearly Correct Model            222
11.4 One Cheer for Causal Inference                        223
11.4.1 Special-Purpose Estimators                     226
11.4.2 Propensity Scores                              230
11.4.3 Sensitivity Analysis of the Selection Process  231
11.4.4 Bounding Treatment Effects                     232
11.4.5 Some Forecasts                                 234
11.5 Some Final Observations                               234
11.5.1 A Police Story                                 234
11.5.2 Regression Analysis as Too Little, Too Late  237
References                                                      239
Index                                                           251