Introduction to Linear Regression Analysis - Douglas C Montgomery

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Résumé :

Preface xiii
About the Companion Website xvi

1. Introduction 1
1.1 Regression and Model Building 1
1.2 Data Collection 5
1.3 Uses of Regression 9
1.4 Role of the Computer 10

2. Simple Linear Regression 12
2.1 Simple Linear Regression Model 12
2.2 Least-Squares Estimation of the Parameters 13
2.3 Hypothesis Testing on the Slope and Intercept 22
2.4 Interval Estimation in Simple Linear Regression 29
2.5 Prediction of New Observations 33
2.6 Coefficient of Determination 35
2.7 A Service Industry Application of Regression 37
2.8 Does Pitching Win Baseball Games? 39
2.9 Using SAS and R for Simple Linear Regression 41
2.10 Some Considerations in the Use of Regression 44
2.11 Regression Through the Origin 46
2.12 Estimation by Maximum Likelihood 52
2.13 Case Where the Regressor x Is Random 53

3. Multiple Linear Regression 69
3.1 Multiple Regression Models 69
3.2 Estimation of the Model Parameters 72
3.3 Hypothesis Testing in Multiple Linear Regression 86
3.4 Confidence Intervals in Multiple Regression 99
3.5 Prediction of New Observations 106
3.6 A Multiple Regression Model for the Patient Satisfaction Data 106
3.7 Does Pitching and Defense Win Baseball Games? 108
3.8 Using SAS and R for Basic Multiple Linear Regression 110
3.9 Hidden Extrapolation in Multiple Regression 111
3.10 Standardized Regression Coefficients 115
3.11 Multicollinearity 121
3.12 Why Do Regression Coefficients Have the Wrong Sign? 123

4. Model Adequacy Checking 134
4.1 Introduction 134
4.2 Residual Analysis 135
4.3 PRESS Statistic 156
4.4 Detection and Treatment of Outliers 157
4.5 Lack of Fit of the Regression Model 161

5. Transformations and Weighting To Correct Model Inadequacies 177
5.1 Introduction 177
5.2 Variance-Stabilizing Transformations 178
5.3 Transformations to Linearize the Model 182
5.4 Analytical Methods for Selecting a Transformation 188
5.5 Generalized and Weighted Least Squares 194
5.6 Regression Models with Random Effects 200

6. Diagnostics for Leverage and Influence 217
6.1 Importance of Detecting Influential Observations 217
6.2 Leverage 218
6.3 Measures of Influence: Cook's D 221
6.4 Measures of Influence: DFFITS and DFBETAS 223
6.5 A Measure of Model Performance 225
6.6 Detecting Groups of Influential Observations 226
6.7 Treatment of Influential Observations 226

7. Polynomial Regression Models 230
7.1 Introduction 230
7.2 Polynomial Models in One Variable 230
7.3 Nonparametric Regression 243
7.4 Polynomial Models in Two or More Variables 249
7.5 Orthogonal Polynomials 255

8. Indicator Variables 268
8.1 General Concept of Indicator Variables 268
8.2 Comments on the Use of Indicator Variables 281
8.3 Regression Approach to Analysis of Variance 283

9. Multicollinearity 293
9.1 Introduction 293
9.2 Sources of Multicollinearity 294
9.3 Effects of Multicollinearity 296
9.4 Multicollinearity Diagnostics 300
9.5 Methods for Dealing with Multicollinearity 311
9.6 Using SAS to Perform Ridge and Principal-Component Regression 336

10. Variable Selection and Model Building 342
10.1 Introduction 342
10.2 Computational Techniques for Variable Selection 353
10.3 Strategy for Variable Selection and Model Building 367
10.4 Case Study: Gorman and Toman Asphalt Data Using SAS 370

11. Validation of Regression Models 388
11.1 Introduction 388
11.2 Validation Techniques 389
11.3 Data from Planned Experiments 401

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