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Regression Analysis by Example, 4th Edition

Book Description

The essentials of regression analysis through practical applications

Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression.

This new edition features the following enhancements:

  • Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis

  • A new chapter entitled Further Topics discusses advanced areas of regression analysis

  • Reorganized, expanded, and upgraded exercises appear at the end of each chapter

  • A fully integrated Web page provides data sets

  • Numerous graphical displays highlight the significance of visual appeal

  • Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R.

    Table of Contents

    1. Cover Page
    2. Title Page
    3. Copyright
    4. Dedication
    5. Contents
    6. PREFACE
    7. CHAPTER 1: INTRODUCTION
      1. 1.1 WHAT IS REGRESSION ANALYSIS?
      2. 1.2 PUBLICLY AVAILABLE DATA SETS
      3. 1.3 SELECTED APPLICATIONS OF REGRESSION ANALYSIS
      4. 1.4 STEPS IN REGRESSION ANALYSIS
      5. 1.5 SCOPE AND ORGANIZATION OF THE BOOK
    8. CHAPTER 2: SIMPLE LINEAR REGRESSION
      1. 2.1 INTRODUCTION
      2. 2.2 COVARIANCE AND CORRELATION COEFFICIENT
      3. 2.3 EXAMPLE: COMPUTER REPAIR DATA
      4. 2.4 THE SIMPLE LINEAR REGRESSION MODEL
      5. 2.5 PARAMETER ESTIMATION
      6. 2.6 TESTS OF HYPOTHESES
      7. 2.7 CONFIDENCE INTERVALS
      8. 2.8 PREDICTIONS
      9. 2.9 MEASURING THE QUALITY OF FIT
      10. 2.10 REGRESSION LINE THROUGH THE ORIGIN
      11. 2.11 TRIVIAL REGRESSION MODELS
      12. 2.12 BIBLIOGRAPHIC NOTES
    9. CHAPTER 3: MULTIPLE LINEAR REGRESSION
      1. 3.1 INTRODUCTION
      2. 3.2 DESCRIPTION OF THE DATA AND MODEL
      3. 3.3 EXAMPLE: SUPERVISOR PERFORMANCE DATA
      4. 3.4 PARAMETER ESTIMATION
      5. 3.5 INTERPRETATIONS OF REGRESSION COEFFICIENTS
      6. 3.6 PROPERTIES OF THE LEAST SQUARES ESTIMATORS
      7. 3.7 MULTIPLE CORRELATION COEFFICIENT
      8. 3.8 INFERENCE FOR INDIVIDUAL REGRESSION COEFFICIENTS
      9. 3.9 TESTS OF HYPOTHESES IN A LINEAR MODEL
      10. 3.10 PREDICTIONS
      11. 3.11 SUMMARY
    10. CHAPTER 4: REGRESSION DIAGNOSTICS: DETECTION OF MODEL VIOLATIONS
      1. 4.1 INTRODUCTION
      2. 4.2 THE STANDARD REGRESSION ASSUMPTIONS
      3. 4.3 VARIOUS TYPES OF RESIDUALS
      4. 4.4 GRAPHICAL METHODS
      5. 4.5 GRAPHS BEFORE FITTING A MODEL
      6. 4.6 GRAPHS AFTER FITTING A MODEL
      7. 4.7 CHECKING LINEARITY AND NORMALITY ASSUMPTIONS
      8. 4.8 LEVERAGE, INFLUENCE, AND OUTLIERS
      9. 4.9 MEASURES OF INFLUENCE
      10. 4.10 THE POTENTIAL-RESIDUAL PLOT
      11. 4.11 WHAT TO DO WITH THE OUTLIERS?
      12. 4.12 ROLE OF VARIABLES IN A REGRESSION EQUATION
      13. 4.13 EFFECTS OF AN ADDITIONAL PREDICTOR
      14. 4.14 ROBUST REGRESSION
    11. CHAPTER 5: QUALITATIVE VARIABLES AS PREDICTORS
      1. 5.1 INTRODUCTION
      2. 5.2 SALARY SURVEY DATA
      3. 5.3 INTERACTION VARIABLES
      4. 5.4 SYSTEMS OF REGRESSION EQUATIONS: COMPARING TWO GROUPS
      5. 5.5 OTHER APPLICATIONS OF INDICATOR VARIABLES
      6. 5.6 SEASONALITY
      7. 5.7 STABILITY OF REGRESSION PARAMETERS OVER TIME
    12. CHAPTER 6: TRANSFORMATION OF VARIABLES
      1. 6.1 INTRODUCTION
      2. 6.2 TRANSFORMATIONS TO ACHIEVE LINEARITY
      3. 6.3 BACTERIA DEATHS DUE TO X-RAY RADIATION
      4. 6.4 TRANSFORMATIONS TO STABILIZE VARIANCE
      5. 6.5 DETECTION OF HETEROSCEDASTIC ERRORS
      6. 6.6 REMOVAL OF HETEROSCEDASTICITY
      7. 6.7 WEIGHTED LEAST SQUARES
      8. 6.8 LOGARITHMIC TRANSFORMATION OF DATA
      9. 6.9 POWER TRANSFORMATION
      10. 6.10 SUMMARY
    13. CHAPTER 7: WEIGHTED LEAST SQUARES
      1. 7.1 INTRODUCTION
      2. 7.2 HETEROSCEDASTIC MODELS
      3. 7.3 TWO-STAGE ESTIMATION
      4. 7.4 EDUCATION EXPENDITURE DATA
      5. 7.5 FITTING A DOSE-RESPONSE RELATIONSHIP CURVE
    14. CHAPTER 8: THE PROBLEM OF CORRELATED ERRORS
      1. 8.1 INTRODUCTION: AUTOCORRELATION
      2. 8.2 CONSUMER EXPENDITURE AND MONEY STOCK
      3. 8.3 DURBIN-WATSON STATISTIC
      4. 8.4 REMOVAL OF AUTOCORRELATION BY TRANSFORMATION
      5. 8.5 ITERATIVE ESTIMATION WITH AUTOCORRELATED ERRORS
      6. 8.6 AUTOCORRELATION AND MISSING VARIABLES
      7. 8.7 ANALYSIS OF HOUSING STARTS
      8. 8.8 LIMITATIONS OF DURBIN-WATSON STATISTIC
      9. 8.9 INDICATOR VARIABLES TO REMOVE SEASONALITY
      10. 8.10 REGRESSING TWO TIME SERIES
    15. CHAPTER 9: ANALYSIS OF COLLINEAR DATA
      1. 9.1 INTRODUCTION
      2. 9.2 EFFECTS ON INFERENCE
      3. 9.3 EFFECTS ON FORECASTING
      4. 9.4 DETECTION OF MULTICOLLINEARITY
      5. 9.5 CENTERING AND SCALING
      6. 9.6 PRINCIPAL COMPONENTS APPROACH
      7. 9.7 IMPOSING CONSTRAINTS
      8. 9.8 SEARCHING FOR LINEAR FUNCTIONS OF THE β 's
      9. 9.9 COMPUTATIONS USING PRINCIPAL COMPONENTS
      10. 9.10 BIBLIOGRAPHIC NOTES
    16. CHAPTER 10: BIASED ESTIMATION OF REGRESSION COEFFICIENTS
      1. 10.1 INTRODUCTION
      2. 10.2 PRINCIPAL COMPONENTS REGRESSION
      3. 10.3 REMOVING DEPENDENCE AMONG THE PREDICTORS
      4. 10.4 CONSTRAINTS ON THE REGRESSION COEFFICIENTS
      5. 10.5 PRINCIPAL COMPONENTS REGRESSION: A CAUTION
      6. 10.6 RIDGE REGRESSION
      7. 10.7 ESTIMATION BY THE RIDGE METHOD
      8. 10.8 RIDGE REGRESSION: SOME REMARKS
      9. 10.9 SUMMARY
      10. Appendix: Ridge Regression
    17. CHAPTER 11: VARIABLE SELECTION PROCEDURES
      1. 11.1 INTRODUCTION
      2. 11.2 FORMULATION OF THE PROBLEM
      3. 11.3 CONSEQUENCES OF VARIABLES DELETION
      4. 11.4 USES OF REGRESSION EQUATIONS
      5. 11.5 CRITERIA FOR EVALUATING EQUATIONS
      6. 11.6 MULTICOLLINEARITY AND VARIABLE SELECTION
      7. 11.7 EVALUATING ALL POSSIBLE EQUATIONS
      8. 11.8 VARIABLE SELECTION PROCEDURES
      9. 11.9 GENERAL REMARKS ON VARIABLE SELECTION METHODS
      10. 11.10 A STUDY OF SUPERVISOR PERFORMANCE
      11. 11.11 VARIABLE SELECTION WITH COLLINEAR DATA
      12. 11.12 THE HOMICIDE DATA
      13. 11.13 VARIABLE SELECTION USING RIDGE REGRESSION
      14. 11.14 SELECTION OF VARIABLES IN AN AIR POLLUTION STUDY
      15. 11.15 A POSSIBLE STRATEGY FOR FITTING REGRESSION MODELS
      16. 11.16 BIBLIOGRAPHIC NOTES
    18. CHAPTER 12: LOGISTIC REGRESSION
      1. 12.1 INTRODUCTION
      2. 12.2 MODELING QUALITATIVE DATA
      3. 12.3 THE LOGIT MODEL
      4. 12.4 EXAMPLE: ESTIMATING PROBABILITY OF BANKRUPTCIES
      5. 12.5 LOGISTIC REGRESSION DIAGNOSTICS
      6. 12.6 DETERMINATION OF VARIABLES TO RETAIN
      7. 12.7 JUDGING THE FIT OF A LOGISTIC REGRESSION
      8. 12.8 THE MULTINOMIAL LOGIT MODEL
      9. 12.9 CLASSIFICATION PROBLEM: ANOTHER APPROACH
    19. CHAPTER 13: FURTHER TOPICS
      1. 13.1 INTRODUCTION
      2. 13.2 GENERALIZED LINEAR MODEL
      3. 13.3 POISSON REGRESSION MODEL
      4. 13.4 INTRODUCTION OF NEW DRUGS
      5. 13.5 ROBUST REGRESSION
      6. 13.6 FITTING A QUADRATIC MODEL
      7. 13.7 DISTRIBUTION OF PCB IN U.S. BAYS
    20. APPENDIX A STATISTICAL TABLES
    21. REFERENCES
    22. INDEX