Regression Analysis (eBook)

Front Cover 1
Regression Analysis: Statistical Modeling of a Response Variable 4
Copyright Page 5
Contents 6
Preface 14
An Overview 20
Part I: The Basics 22
Chapter 1. The Analysis of Means: A Review of Basics and an Introduction to Linear Models 26
1.1 Introduction 26
1.2 Sampling Distributions 26
1.3 Inferences on a Single Population Mean 30
1.4 Inferences on Two Means Using Independent Samples 38
1.5 Inferences on Several Means 44
1.6 Summary 49
1.7 Chapter Exercises 51
Chapter 2. Simple Linear Regression: Linear Regression with one Independent Variable 56
2.1 Introduction 56
2.2 The Linear Regression Model 58
2.3 Inferences on the Parameters ß0 and ß1 61
2.4 Inferences on the Response Variable 70
2.5 Correlation and the Coefficient of Determination 73
2.6 Regression through the Origin 77
2.7 Assumptions on the Simple Linear Regression Model 83
2.8 Uses and Misuses of Regression 86
2.9 Inverse Predictions 86
2.10 Summary 88
2.11 Chapter Exercises 89
Chapter 3. Multiple Linear Regression 94
3.1 Introduction 94
3.2 The Multiple Linear Regression Model 95
3.3 Estimation of Coefficients 97
3.4 Interpreting the Partial Regression Coef.cients 102
3.5 Inferences on the Parameters 106
3.6 Testing a General Linear Hypothesis (Optional Topic) 118
3.7 Inferences on the Response Variable in Multiple Regression 121
3.8 Correlation and the Coef.cient of Determination 123
3.9 Getting Results 126
3.10 Summary and a Look Ahead 127
3.11 Chapter Exercises 129
Part II: Problems and Remedies 138
Chapter 4. Problems with Observations 140
4.1 Introduction 140
4.2 Outliers and Influential Observations 141
4.3 Unequal Variances 164
4.4 Robust Estimation 177
4.5 Correlated Errors 181
4.6 Summary 193
4.7 Chapter Exercises 194
Chapter 5. Multicollinearity 198
5.1 Introduction 198
5.2 The Effects of Multicollinearity 200
5.3 Diagnosing Multicollinearity 211
5.4 Remedial Methods 219
5.5 Summary 242
5.6 Chapter Exercises 243
Chapter 6. Problems with the Model 248
6.1 Introduction 248
6.2 Specification Error 249
6.3 Lack of Fit Test 253
6.4 Overspeci.cation: Too Many Variables 259
6.5 Variable Selection Procedures 261
6.6 Reliability of Variable Selection 271
6.7 Usefulness of Variable Selection 277
6.8 Variable Selection and Influential Observations 280
6.9 Summary 283
6.10 Chapter Exercises 283
Part III: Additional Uses of Regression 288
Chapter 7. Curve Fitting 290
7.1 Introduction 290
7.2 Polynomial Models with One Independent Variable 291
7.3 Segmented Polynomials with Known Knots 300
7.4 Polynomial Regression in Several Variables Response Surfaces
7.5 Curve Fitting without a Model 313
7.6 Summary 318
7.7 Chapter Exercises 318
Chapter 8. Introduction to Nonlinear Models 324
8.1 Introduction 324
8.2 Intrinsically Linear Models 326
8.3 Intrinsically Nonlinear Models 341
8.4 Summary 353
8.5 Chapter Exercises 354
Chapter 9. Indicator Variables 358
9.1 Introduction 358
9.2 The Dummy Variable Model 360
9.3 Unequal Cell Frequencies 367
9.4 Empty Cells 372
9.5 Models with Dummy and Continuous Variables 375
9.6 A Special Application: The Analysis of Covariance 380
9.7 Heterogeneous Slopes in the Analysis of Covariance 384
9.8 Summary 389
9.9 Chapter Exercises 389
Chapter 10. Categorical Response Variables 392
10.1 Introduction 392
10.2 Binary Response Variables 392
10.3 Weighted Least Squares 395
10.4 Simple Logistic Regression 400
10.5 Multiple Logistic Regression 406
10.6 Loglinear Model 409
10.7 Summary 416
10.8 Chapter Exercises 417
Chapter 11. Generalized Linear Models 422
11.1 Introduction 422
11.2 The Link Function 424
11.3 The Logistic Model 425
11.4 Other Models 427
11.5 Summary 431
Appendix A: Statistical Tables 434
A.1 The Standard Normal Distribution—Probabilities Exceeding Z 435
A.2 The T Distribution—Values of T Exceeded with Given Probability 440
A.3 The X2 Distribution—X2 Values Exceeded with Given Probability 441
A.4 The F Distribution p= 0.1 442
A.5 The Durbin–Watson Test Bounds 452
Appendix B: A Brief Introduction Tomatrices 454
B.1 Matrix Algebra 455
B.2 Solving Linear Equations 458
Appendix C: Estimation Procedures 460
C.1 Least Squares Estimation 460
C.2 Maximum Likelihood Estimation 462
References 466
Index 470