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Introduction to Linear Regression Analysis, 5th Edition

Book Description

Praise for the Fourth Edition

"As with previous editions, the authors have produced a leading textbook on regression."

—Journal of the American Statistical Association

A comprehensive and up-to-date introduction to the fundamentals of regression analysis

Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today's cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences.

Following a general introduction to regression modeling, including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics, including:

  • A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models

  • Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model

  • Tests on individual regression coefficients and subsets of coefficients

  • Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data.

  • In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition. Numerous exercises have been added throughout, allowing readers to test their understanding of the material, and a related FTP site features the presented data sets, extensive problem solutions, software hints, and PowerPoint slides to facilitate instructional use of the book.

    Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences.

    Table of Contents

    1. Cover Page
    2. Title Page
    3. Copyright
    4. Contents
    5. PREFACE
    6. CHAPTER 1: INTRODUCTION
      1. 1.1 REGRESSION AND MODEL BUILDING
      2. 1.2 DATA COLLECTION
      3. 1.3 USES OF REGRESSION
      4. 1.4 ROLE OF THE COMPUTER
    7. CHAPTER 2: SIMPLE LINEAR REGRESSION
      1. 2.1 SIMPLE LINEAR REGRESSION MODEL
      2. 2.2 LEAST-SQUARES ESTIMATION OF THE PARAMETERS
      3. 2.3 HYPOTHESIS TESTING ON THE SLOPE AND INTERCEPT
      4. 2.4 INTERVAL ESTIMATION IN SIMPLE LINEAR REGRESSION
      5. 2.5 PREDICTION OF NEW OBSERVATIONS
      6. 2.6 COEFFICIENT OF DETERMINATION
      7. 2.7 A SERVICE INDUSTRY APPLICATION OF REGRESSION
      8. 2.8 USING SAS® AND R FOR SIMPLE LINEAR REGRESSION
      9. 2.9 SOME CONSIDERATIONS IN THE USE OF REGRESSION
      10. 2.10 REGRESSION THROUGH THE ORIGIN
      11. 2.11 ESTIMATION BY MAXIMUM LIKELIHOOD
      12. 2.12 CASE WHERE THE REGRESSOR x IS RANDOM
      13. PROBLEMS
    8. CHAPTER 3: MULTIPLE LINEAR REGRESSION
      1. 3.1 MULTIPLE REGRESSION MODELS
      2. 3.2 ESTIMATION OF THE MODEL PARAMETERS
      3. 3.3 HYPOTHESIS TESTING IN MULTIPLE LINEAR REGRESSION
      4. 3.4 CONFIDENCE INTERVALS IN MULTIPLE REGRESSION
      5. 3.5 PREDICTION OF NEW OBSERVATIONS
      6. 3.6 A MULTIPLE REGRESSION MODEL FOR THE PATIENT SATISFACTION DATA
      7. 3.7 USING SAS AND R FOR BASIC MULTIPLE LINEAR REGRESSION
      8. 3.8 HIDDEN EXTRAPOLATION IN MULTIPLE REGRESSION
      9. 3.9 STANDARDIZED REGRESSION COEFFLCIENTS
      10. 3.10 MULTICOLLINEARITY
      11. 3.11 WHY DO REGRESSION COEFFICIENTS HAVE THE WRONG SIGN?
      12. PROBLEMS
    9. CHAPTER 4: MODEL ADEQUACY CHECKING
      1. 4.1 INTRODUCTION
      2. 4.2 RESIDUAL ANALYSIS
      3. 4.3 PRESS STATISTIC
      4. 4.4 DETECTION AND TREATMENT OF OUTLIERS
      5. 4.5 LACK OF FIT OF THE REGRESSION MODEL
      6. PROBLEMS
    10. CHAPTER 5: TRANSFORMATIONS AND WEIGHTING TO CORRECT MODEL INADEQUACIES
      1. 5.1 INTRODUCTION
      2. 5.2 VARIANCE-STABILIZING TRANSFORMATIONS
      3. 5.3 TRANSFORMATIONS TO LINEARIZE THE MODEL
      4. 5.4 ANALYTICAL METHODS FOR SELECTING A TRANSFORMATION
      5. 5.5 GENERALIZED AND WEIGHTED LEAST SQUARES
      6. 5.6 REGRESSION MODELS WITH RANDOM EFFECTS
      7. PROBLEMS
    11. CHAPTER 6: DIAGNOSTICS FOR LEVERAGE AND INFLUENCE
      1. 6.1 IMPORTANCE OF DETECTING INFLUENTIAL OBSERVATIONS
      2. 6.2 LEVERAGE
      3. 6.3 MEASURES OF INFLUENCE: COOK'S D
      4. 6.4 MEASURES OF INFLUENCE: DFFITS AND DFBETAS
      5. 6.5 A MEASURE OF MODEL PERFORMANCE
      6. 6.6 DETECTING GROUPS OF INFLUENTIAL OBSERVATIONS
      7. 6.7 TREATMENT OF INFLUENTIAL OBSERVATIONS
      8. PROBLEMS
    12. CHAPTER 7: POLYNOMIAL REGRESSION MODELS
      1. 7.1 INTRODUCTION
      2. 7.2 POLYNOMIAL MODELS IN ONE VARIABLE
      3. 7.3 NONPARAMETRIC REGRESSION
      4. 7.4 POLYNOMIAL MODELS IN TWO OR MORE VARIABLES
      5. 7.5 ORTHOGONAL POLYNOMIALS
      6. PROBLEMS
    13. CHAPTER 8: INDICATOR VARIABLES
      1. 8.1 GENERAL CONCEPT OF INDICATOR VARIABLES
      2. 8.2 COMMENTS ON THE USE OF INDICATOR VARIABLES
      3. 8.3 REGRESSION APPROACH TO ANALYSIS OF VARIANCE
      4. PROBLEMS
    14. CHAPTER 9: MULTICOLLINEARITY
      1. 9.1 INTRODUCTION
      2. 9.2 SOURCES OF MULTICOLLINEARITY
      3. 9.3 EFFECTS OF MULTICOLLINEARITY
      4. 9.4 MULTICOLLINEARITY DIAGNOSTICS
      5. 9.5 METHODS FOR DEALING WITH MULTICOLLINEARITY
      6. 9.6 USING SAS TO PERFORM RIDGE AND PRINCIPAL-COMPONENT REGRESSION
      7. PROBLEMS
    15. CHAPTER 10: VARIABLE SELECTION AND MODEL BUILDING
      1. 10.1 INTRODUCTION
      2. 10.2 COMPUTATIONAL TECHNIQUES FOR VARIABLE SELECTION
      3. 10.3 STRATEGY FOR VARIABLE SELECTION AND MODEL BUILDING
      4. 10.4 CASE STUDY: GORMAN AND TOMAN ASPHALT DATA USING SAS
      5. PROBLEMS
    16. CHAPTER 11: VALIDATION OF REGRESSION MODELS
      1. 11.1 INTRODUCTION
      2. 11.2 VALIDATION TECHNIQUES
      3. 11.3 DATA FROM PLANNED EXPERIMENTS
      4. PROBLEMS
    17. CHAPTER 12: INTRODUCTION TO NONLINEAR REGRESSION
      1. 12.1 LINEAR AND NONLINEAR REGRESSION MODELS
      2. 12.2 ORIGINS OF NONLINEAR MODELS
      3. 12.3 NONLINEAR LEAST SQUARES
      4. 12.4 TRANFORMATION TO A LINEAR MODEL
      5. 12.5 PARAMETER ESTIMATION IN A NONLINEAR SYSTEM
      6. 12.6 STATISTICAL INFERENCE IN NONLINEAR REGRESSION
      7. 12.7 EXAMPLES OF NONLINEAR REGRESSION MODELS
      8. 12.8 USING SAS AND R
      9. PROBLEMS
    18. CHAPTER 13: GENERALIZED LINEAR MODELS
      1. 13.1 INTRODUCTION
      2. 13.2 LOGISTIC REGRESSION MODELS
      3. 13.3 POISSON REGRESSION
      4. 13.4 THE GENERALIZED LINEAR MODEL
      5. PROBLEMS
    19. CHAPTER 14: REGRESSION ANALYSIS OF TIME SERIES DATA
      1. 14.1 INTRODUCTION TO REGRESSION MODELS FOR TIME SERIES DATA
      2. 14.2 DETECTING AUTOCORRELATION: THE DURBIN–WATSON TEST
      3. 14.3 ESTIMATING THE PARAMETERS IN TIME SERIES REGRESSION MODELS
      4. PROBLEMS
    20. CHAPTER 15: OTHER TOPICS IN THE USE OF REGRESSION ANALYSIS
      1. 15.1 ROBUST REGRESSION
      2. 15.2 EFFECT OF MEASUREMENT ERRORS IN THE REGRESSORS
      3. 15.3 INVERSE ESTIMATION—THE CALIBRATION PROBLEM
      4. 15.4 BOOTSTRAPPING IN REGRESSION
      5. 15.5 CLASSIFICATION AND REGRESSION TREES (CART)
      6. 15.6 NEURAL NETWORKS
      7. 15.7 DESIGNED EXPERIMENTS FOR REGRESSION
      8. PROBLEMS
    21. APPENDIX A: STATISTICAL TABLES
    22. APPENDIX B: DATA SETS FOR EXERCISES
    23. APPENDIX C: SUPPLEMENTAL TECHNICAL MATERIAL
      1. C.1 BACKGROUND ON BASIC TEST STATISTICS
      2. C.2 BACKGROUND FROM THE THEORY OF LINEAR MODELS
      3. C.3 IMPORTANT RESULTS ON SS R AND SS RES
      4. C.4 GAUSS–MARKOV THEOREM, VAR(ε) = σ2I
      5. C.5 COMPUTATIONAL ASPECTS OF MULTIPLE REGRESSION
      6. C.6 RESULT ON THE INVERSE OF A MATRIX
      7. C.7 DEVELOPMENT OF THE PRESS STATISTIC
      8. C.8 DEVELOPMENT OF S2(i)
      9. C.9 OUTLIER TEST BASED ON R-STUDENT
      10. C.10 INDEPENDENCE OF RESIDUALS AND FITTED VALUES
      11. C.11 GAUSS-MARKOV THEOREM, VAR(ε) = V
      12. C.12 BIAS IN MS RES WHEN THE MODEL IS UNDERSPECIFIED
      13. C.13 COMPUTATION OF INFLUENCE DIAGNOSTICS
      14. C.14 GENERALIZED LINEAR MODELS
    24. APPENDIX D: INTRODUCTION TO SAS
      1. D.1 BASIC DATA ENTRY
      2. D.2 CREATING PERMANENT SAS DATA SETS
      3. D.3 IMPORTING DATA FROM AN EXCEL FILE
      4. D.4 OUTPUT COMMAND
      5. D.5 LOG FILE
      6. D.6 ADDING VARIABLES TO AN EXISTING SAS DATA SET
    25. APPENDIX E: INTRODUCTION TO R TO PERFORM LINEAR REGRESSION ANALYSIS
      1. E.1 Basic Background on R
      2. E.2 Basic Data Entry
      3. E.3 Brief Comments on Other Functionality in R
      4. E.4 R Commander
    26. REFERENCES
    27. INDEX