Lavoisier S.A.S.
14 rue de Provigny
94236 Cachan cedex
FRANCE

Heures d'ouverture 08h30-12h30/13h30-17h30
Tél.: +33 (0)1 47 40 67 00
Fax: +33 (0)1 47 40 67 02


Url canonique : www.lavoisier.fr/livre/mathematiques/introduction-to-linear-regression-analysis/descriptif_4502116
Url courte ou permalien : www.lavoisier.fr/livre/notice.asp?ouvrage=4502116

Introduction to Linear Regression Analysis (6th Ed.) Wiley Series in Probability and Statistics Series

Langue : Anglais

Auteurs :

Couverture de l’ouvrage Introduction to Linear Regression Analysis
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.

    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

    2.2.1 Estimation of β0 and β1 13

    2.2.2 Properties of the Least-Squares Estimators and the Fitted Regression Model 18

    2.2.3 Estimation of σ2 20

    2.2.4 Alternate Form of the Model 22

    2.3 Hypothesis Testing on the Slope and Intercept 22

    2.3.1 Use of t Tests 22

    2.3.2 Testing Significance of Regression 24

    2.3.3 Analysis of Variance 25

    2.4 Interval Estimation in Simple Linear Regression 29

    2.4.1 Confidence Intervals on β0, β1, and σ2 29

    2.4.2 Interval Estimation of the Mean Response 30

    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

    2.13.1 x and y Jointly Distributed 54

    2.13.2 x and y Jointly Normally Distributed: Correlation Model 54

    Problems 59

    3. Multiple Linear Regression 69

    3.1 Multiple Regression Models 69

    3.2 Estimation of the Model Parameters 72

    3.2.1 Least-Squares Estimation of the Regression Coefficients 72

    3.2.2 Geometrical Interpretation of Least Squares 79

    3.2.3 Properties of the Least-Squares Estimators 81

    3.2.4 Estimation of σ2 82

    3.2.5 Inadequacy of Scatter Diagrams in Multiple Regression 84

    3.2.6 Maximum-Likelihood Estimation 85

    3.3 Hypothesis Testing in Multiple Linear Regression 86

    3.3.1 Test for Significance of Regression 86

    3.3.2 Tests on Individual Regression Coefficients and Subsets of Coefficients 90

    3.3.3 Special Case of Orthogonal Columns in X 95

    3.3.4 Testing the General Linear Hypothesis 97

    3.4 Confidence Intervals in Multiple Regression 99

    3.4.1 Confidence Intervals on the Regression Coefficients 100

    3.4.2 ci Estimation of the Mean Response 101

    3.4.3 Simultaneous Confidence Intervals on Regression Coefficients 102

    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

    Problems 125

    4. Model Adequacy Checking 134

    4.1 Introduction 134

    4.2 Residual Analysis 135

    4.2.1 Definition of Residuals 135

    4.2.2 Methods for Scaling Residuals 135

    4.2.3 Residual Plots 141

    4.2.4 Partial Regression and Partial Residual Plots 148

    4.2.5 Using Minitab®, SAS, and R for Residual Analysis 151

    4.2.6 Other Residual Plotting and Analysis Methods 154

    4.3 PRESS Statistic 156

    4.4 Detection and Treatment of Outliers 157

    4.5 Lack of Fit of the Regression Model 161

    4.5.1 A Formal Test for Lack of Fit 161

    4.5.2 Estimation of Pure Error from Near Neighbors 165

    Problems 170

    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

    5.4.1 Transformations on y: The Box–Cox Method 188

    5.4.2 Transformations on the Regressor Variables 190

    5.5 Generalized and Weighted Least Squares 194

    5.5.1 Generalized Least Squares 194

    5.5.2 Weighted Least Squares 196

    5.5.3 Some Practical Issues 197

    5.6 Regression Models with Random Effects 200

    5.6.1 Subsampling 200

    5.6.2 The General Situation for a Regression Model with a Single Random Effect 204

    5.6.3 The Importance of the Mixed Model in Regression 208

    Problems 208

    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

    Problems 227

    7. Polynomial Regression Models 230

    7.1 Introduction 230

    7.2 Polynomial Models in One Variable 230

    7.2.1 Basic Principles 230

    7.2.2 Piecewise Polynomial Fitting (Splines) 236

    7.2.3 Polynomial and Trigonometric Terms 242

    7.3 Nonparametric Regression 243

    7.3.1 Kernel Regression 244

    7.3.2 Locally Weighted Regression (Loess) 244

    7.3.3 Final Cautions 249

    7.4 Polynomial Models in Two or More Variables 249

    7.5 Orthogonal Polynomials 255

    Problems 261

    8. Indicator Variables 268

    8.1 General Concept of Indicator Variables 268

    8.2 Comments on the Use of Indicator Variables 281

    8.2.1 Indicator Variables versus Regression on Allocated Codes 281

    8.2.2 Indicator Variables as a Substitute for a Quantitative Regressor 282

    8.3 Regression Approach to Analysis of Variance 283

    Problems 288

    9. Multicollinearity 293

    9.1 Introduction 293

    9.2 Sources of Multicollinearity 294

    9.3 Effects of Multicollinearity 296

    9.4 Multicollinearity Diagnostics 300

    9.4.1 Examination of the Correlation Matrix 300

    9.4.2 Variance Inflation Factors 304

    9.4.3 Eigensystem Analysis of XʹX 305

    9.4.4 Other Diagnostics 310

    9.4.5 SAS and R Code for Generating Multicollinearity Diagnostics 311

    9.5 Methods for Dealing with Multicollinearity 311

    9.5.1 Collecting Additional Data 311

    9.5.2 Model Respecification 312

    9.5.3 Ridge Regression 312

    9.5.4 Principal-Component Regression 329

    9.5.5 Comparison and Evaluation of Biased Estimators 334

    9.6 Using SAS to Perform Ridge and Principal-Component Regression 336

    Problems 338

    10. Variable Selection and Model Building 342

    10.1 Introduction 342

    10.1.1 Model-Building Problem 342

    10.1.2 Consequences of Model Misspecification 344

    10.1.3 Criteria for Evaluating Subset Regression Models 347

    10.2 Computational Techniques for Variable Selection 353

    10.2.1 All Possible Regressions 353

    10.2.2 Stepwise Regression Methods 359

    10.3 Strategy for Variable Selection and Model Building 367

    10.4 Case Study: Gorman and Toman Asphalt Data Using SAS 370

    Problems 383

    11. Validation of Regression Models 388

    11.1 Introduction 388

    11.2 Validation Techniques 389

    11.2.1 Analysis of Model Coefficients and Predicted Values 389

    11.2.2 Collecting Fresh Data—Confirmation Runs 391

    11.2.3 Data Splitting 393

    11.3 Data from Planned Experiments 401

    Problems 402

    12. Introduction to Nonlinear Regression 405

    12.1 Linear and Nonlinear Regression Models 405

    12.1.1 Linear Regression Models 405

    12.1.2 Nonlinear Regression Models 406

    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

    12.5.1 Linearization 416

    12.5.2 Other Parameter Estimation Methods 423

    12.5.3 Starting Values 424

    12.6 Statistical Inference in Nonlinear Regression 425

    12.7 Examples of Nonlinear Regression Models 427

    12.8 Using SAS and R 428

    Problems 432

    13. Generalized Linear Models 440

    13.1 Introduction 440

    13.2 Logistic Regression Models 441

    13.2.1 Models with a Binary Response Variable 441

    13.2.2 Estimating the Parameters in a Logistic Regression Model 442

    13.2.3 Interpretation of the Parameters in a Logistic Regression Model 447

    13.2.4 Statistical Inference on Model Parameters 449

    13.2.5 Diagnostic Checking in Logistic Regression 459

    13.2.6 Other Models for Binary Response Data 461

    13.2.7 More Than Two Categorical Outcomes 461

    13.3 Poisson Regression 463

    13.4 The Generalized Linear Model 469

    13.4.1 Link Functions and Linear Predictors 470

    13.4.2 Parameter Estimation and Inference in the GLM 471

    13.4.3 Prediction and Estimation with the GLM 473

    13.4.4 Residual Analysis in the GLM 475

    13.4.5 Using R to Perform GLM Analysis 477

    13.4.6 Overdispersion 480

    Problems 481

    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

    Problems 517

    15. Other Topics in the Use of Regression Analysis 521

    15.1 Robust Regression 521

    15.1.1 Need for Robust Regression 521

    15.1.2 M-Estimators 524

    15.1.3 Properties of Robust Estimators 531

    15.2 Effect of Measurement Errors in the Regressors 532

    15.2.1 Simple Linear Regression 532

    15.2.2 The Berkson Model 534

    15.3 Inverse Estimation—The Calibration Problem 534

    15.4 Bootstrapping in Regression 538

    15.4.1 Bootstrap Sampling in Regression 539

    15.4.2 Bootstrap Confidence Intervals 540

    15.5 Classification and Regression Trees (CART) 545

    15.6 Neural Networks 547

    15.7 Designed Experiments for Regression 549

    Problems 557

    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(ε) = σ 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(ε) = 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

    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.

    Date de parution :

    Ouvrage de 704 p.

    18x25.7 cm

    Disponible chez l'éditeur (délai d'approvisionnement : 14 jours).

    144,47 €

    Ajouter au panier