Introduction to Linear Regression Analysis

6th Auflage
ISBN: 978-1-119-57872-7
Verlag: John Wiley & Sons

Buch, Englisch, 704 Seiten, Format (B × H): 187 mm x 259 mm, Gewicht: 1275 g

INTRODUCTION TO LINEAR REGRESSION ANALYSIS

A comprehensive and current introduction to the fundamentals of regression analysis

Introduction to Linear Regression Analysis, 6th Edition is the most comprehensive, fulsome, and current examination of the foundations of linear regression analysis. Fully updated in this new sixth edition, the distinguished authors have included new material on generalized regression techniques and new examples to help the reader understand retain the concepts taught in the book.

The new edition focuses on four key areas of improvement over the fifth edition: - New exercises and data sets
- New material on generalized regression techniques
- The inclusion of JMP software in key areas
- Carefully condensing the text where possible

Introduction to Linear Regression Analysis skillfully blends theory and application in both the conventional and less common uses of regression analysis in today’s cutting-edge scientific research. The text equips readers to understand the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences.

Autoren/Hrsg.

Montgomery, Douglas C.

Peck, Elizabeth A.

Vining, G. Geoffrey

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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

12. Introduction to Nonlinear Regression 405
12.1 Linear and Nonlinear Regression Models 405
12.2 Origins of Nonlinear Models 407
12.3 Nonlinear Least Squares 411
12.4 Transformation to a Linear Model 413
12.5 Parameter Estimation in a Nonlinear System 416
12.6 Statistical Inference in Nonlinear Regression 425
12.7 Examples of Nonlinear Regression Models 427
12.8 Using SAS and R 428

13. Generalized Linear Models 440
13.1 Introduction 440
13.2 Logistic Regression Models 441
13.3 Poisson Regression 463
13.4 The Generalized Linear Model 469

14. Regression Analysis of Time Series Data 495
14.1 Introduction to Regression Models for Time Series Data 495
14.2 Detecting Autocorrelation: The Durbin–Watson Test 496
14.3 Estimating the Parameters in Time Series Regression Models 501

15. Other Topics in the Use of Regression Analysis 521
15.1 Robust Regression 521
15.2 Effect of Measurement Errors in the Regressors 532
15.3 Inverse Estimation—The Calibration Problem 534
15.4 Bootstrapping in Regression 538
15.5 Classification and Regression Trees (CART) 545
15.6 Neural Networks 547
15.7 Designed Experiments for Regression 549

Appendix A. Statistical Tables 561

Appendix B. Data Sets for Exercises 573

Appendix C. Supplemental Technical Material 602
C.1 Background on Basic Test Statistics 602
C.2 Background from the Theory of Linear Models 605
C.3 Important Results on SS R and SS Res 609
C.4 Gauss-Markov Theorem, Var(e) = s 2 I 615
C.5 Computational Aspects of Multiple Regression 617
C.6 Result on the Inverse of a Matrix 618
C.7 Development of the PRESS Statistic 619
C.8 Development of S(i) 2 621
C.9 Outlier Test Based on R-Student 622
C.10 Independence of Residuals and Fitted Values 624
C.11 Gauss–Markov Theorem, Var(e) = V 625
C.12 Bias in MSRes When the Model Is Underspecified 627
C.13 Computation of Influence Diagnostics 628
C.14 Generalized Linear Models 629

Appendix D. Introduction to SAS 641
D.1 Basic Data Entry 642
D.2 Creating Permanent SAS Data Sets 646
D.3 Importing Data from an EXCEL File 647
D.4 Output Command 648
D.5 Log File 648
D.6 Adding Variables to an Existing SAS Data Set 650

Appendix E. Introduction to R to Perform Linear Regression Analysis 651
E.1 Basic Background on R 651
E.2 Basic Data Entry 652
E.3 Brief Comments on Other Functionality in R 654
E.4 R Commander 655

References 656
Index 670

Über Autor(innen)

DOUGLAS C. MONTGOMERY, PHD, is Regents Professor of Industrial Engineering and Statistics at Arizona State University. Dr. Montgomery is the co-author of several Wiley books including Introduction to Linear Regression Analysis, 5th Edition.

ELIZABETH A. PECK, PHD, is Logistics Modeling Specialist at the Coca-Cola Company in Atlanta, Georgia.

G. GEOFFREY VINING, PHD, is Professor in the Department of Statistics at Virginia Polytechnic and State University. Dr. Peck is co-author of Introduction to Linear Regression Analysis, 5th Edition.