Regression Analysis, Second Edition

The book provides complete coverage of the classical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design. * Examples and exercises contain real data and graphical illustration for ease of interpretation * Outputs from SAS 7, SPSS 7, Excel, and Minitab are used for illustration, but any major statistical software package will work equally well. * Data sets are furnished on CD included in the text Regression Analysis: Statistical Modeling of a Response Variable......Page 4 Copyright Page......Page 5 Contents......Page 6 Preface......Page 14 An Overview......Page 20 Part I: The Basics......Page 22 1.2 Sampling Distributions......Page 26 1.3 Inferences on a Single Population Mean......Page 30 1.4 Inferences on Two Means Using Independent Samples......Page 38 1.5 Inferences on Several Means......Page 44 1.6 Summary......Page 49 1.7 Chapter Exercises......Page 51 2.1 Introduction......Page 56 2.2 The Linear Regression Model......Page 58 2.3 Inferences on the Parameters ß0 and ß1......Page 61 2.4 Inferences on the Response Variable......Page 70 2.5 Correlation and the Coefficient of Determination......Page 73 2.6 Regression through the Origin......Page 77 2.7 Assumptions on the Simple Linear Regression Model......Page 83 2.9 Inverse Predictions......Page 86 2.10 Summary......Page 88 2.11 Chapter Exercises......Page 89 3.1 Introduction......Page 94 3.2 The Multiple Linear Regression Model......Page 95 3.3 Estimation of Coefficients......Page 97 3.4 Interpreting the Partial Regression Coef.cients......Page 102 3.5 Inferences on the Parameters......Page 106 3.6 Testing a General Linear Hypothesis (Optional Topic)......Page 118 3.7 Inferences on the Response Variable in Multiple Regression......Page 121 3.8 Correlation and the Coef.cient of Determination......Page 123 3.9 Getting Results......Page 126 3.10 Summary and a Look Ahead......Page 127 3.11 Chapter Exercises......Page 129 Part II: Problems and Remedies......Page 138 4.1 Introduction......Page 140 4.2 Outliers and Influential Observations......Page 141 4.3 Unequal Variances......Page 164 4.4 Robust Estimation......Page 177 4.5 Correlated Errors......Page 181 4.6 Summary......Page 193 4.7 Chapter Exercises......Page 194 5.1 Introduction......Page 198 5.2 The Effects of Multicollinearity......Page 200 5.3 Diagnosing Multicollinearity......Page 211 5.4 Remedial Methods......Page 219 5.5 Summary......Page 242 5.6 Chapter Exercises......Page 243 6.1 Introduction......Page 248 6.2 Specification Error......Page 249 6.3 Lack of Fit Test......Page 253 6.4 Overspeci.cation: Too Many Variables......Page 259 6.5 Variable Selection Procedures......Page 261 6.6 Reliability of Variable Selection......Page 271 6.7 Usefulness of Variable Selection......Page 277 6.8 Variable Selection and Influential Observations......Page 280 6.10 Chapter Exercises......Page 283 Part III: Additional Uses of Regression......Page 288 7.1 Introduction......Page 290 7.2 Polynomial Models with One Independent Variable......Page 291 7.3 Segmented Polynomials with Known Knots......Page 300 7.4 Polynomial Regression in Several Variables; Response Surfaces......Page 304 7.5 Curve Fitting without a Model......Page 313 7.7 Chapter Exercises......Page 318 8.1 Introduction......Page 324 8.2 Intrinsically Linear Models......Page 326 8.3 Intrinsically Nonlinear Models......Page 341 8.4 Summary......Page 353 8.5 Chapter Exercises......Page 354 9.1 Introduction......Page 358 9.2 The Dummy Variable Model......Page 360 9.3 Unequal Cell Frequencies......Page 367 9.4 Empty Cells......Page 372 9.5 Models with Dummy and Continuous Variables......Page 375 9.6 A Special Application: The Analysis of Covariance......Page 380 9.7 Heterogeneous Slopes in the Analysis of Covariance......Page 384 9.9 Chapter Exercises......Page 389 10.2 Binary Response Variables......Page 392 10.3 Weighted Least Squares......Page 395 10.4 Simple Logistic Regression......Page 400 10.5 Multiple Logistic Regression......Page 406 10.6 Loglinear Model......Page 409 10.7 Summary......Page 416 10.8 Chapter Exercises......Page 417 11.1 Introduction......Page 422 11.2 The Link Function......Page 424 11.3 The Logistic Model......Page 425 11.4 Other Models......Page 427 11.5 Summary......Page 431 Appendix A: Statistical Tables......Page 434 A.1 The Standard Normal Distribution—Probabilities Exceeding Z......Page 435 A.2 The T Distribution—Values of T Exceeded with Given Probability......Page 440 A.3 The X2 Distribution—X2 Values Exceeded with Given Probability......Page 441 A.4 The F Distribution p= 0.1......Page 442 A.5 The Durbin–Watson Test Bounds......Page 452 Appendix B: A Brief Introduction Tomatrices......Page 454 B.1 Matrix Algebra......Page 455 B.2 Solving Linear Equations......Page 458 C.1 Least Squares Estimation......Page 460 C.2 Maximum Likelihood Estimation......Page 462 References......Page 466 Index......Page 470 Regression Analysis: Statistical Modeling of a Response Variable 4 Copyright Page 5 Contents 6 Preface 14 An Overview 20 Part I: The Basics 22 Chapter 1. The Analysis of Means: A Review of Basics and an Introduction to Linear Models 26 1.1 Introduction 26 1.2 Sampling Distributions 26 1.3 Inferences on a Single Population Mean 30 1.4 Inferences on Two Means Using Independent Samples 38 1.5 Inferences on Several Means 44 1.6 Summary 49 1.7 Chapter Exercises 51 Chapter 2. Simple Linear Regression: Linear Regression with one Independent Variable 56 2.1 Introduction 56 2.2 The Linear Regression Model 58 2.3 Inferences on the Parameters ß0 and ß1 61 2.4 Inferences on the Response Variable 70 2.5 Correlation and the Coefficient of Determination 73 2.6 Regression through the Origin 77 2.7 Assumptions on the Simple Linear Regression Model 83 2.8 Uses and Misuses of Regression 86 2.9 Inverse Predictions 86 2.10 Summary 88 2.11 Chapter Exercises 89 Chapter 3. Multiple Linear Regression 94 3.1 Introduction 94 3.2 The Multiple Linear Regression Model 95 3.3 Estimation of Coefficients 97 3.4 Interpreting the Partial Regression Coef.cients 102 3.5 Inferences on the Parameters 106 3.6 Testing a General Linear Hypothesis (Optional Topic) 118 3.7 Inferences on the Response Variable in Multiple Regression 121 3.8 Correlation and the Coef.cient of Determination 123 3.9 Getting Results 126 3.10 Summary and a Look Ahead 127 3.11 Chapter Exercises 129 Part II: Problems and Remedies 138 Chapter 4. Problems with Observations 140 4.1 Introduction 140 4.2 Outliers and Influential Observations 141 4.3 Unequal Variances 164 4.4 Robust Estimation 177 4.5 Correlated Errors 181 4.6 Summary 193 4.7 Chapter Exercises 194 Chapter 5. Multicollinearity 198 5.1 Introduction 198 5.2 The Effects of Multicollinearity 200 5.3 Diagnosing Multicollinearity 211 5.4 Remedial Methods 219 5.5 Summary 242 5.6 Chapter Exercises 243 Chapter 6. Problems with the Model 248 6.1 Introduction 248 6.2 Specification Error 249 6.3 Lack of Fit Test 253 6.4 Overspeci.cation: Too Many Variables 259 6.5 Variable Selection Procedures 261 6.6 Reliability of Variable Selection 271 6.7 Usefulness of Variable Selection 277 6.8 Variable Selection and Influential Observations 280 6.9 Summary 283 6.10 Chapter Exercises 283 Part III: Additional Uses of Regression 288 Chapter 7. Curve Fitting 290 7.1 Introduction 290 7.2 Polynomial Models with One Independent Variable 291 7.3 Segmented Polynomials with Known Knots 300 7.4 Polynomial Regression in Several Variables; Response Surfaces 304 7.5 Curve Fitting without a Model 313 7.6 Summary 318 7.7 Chapter Exercises 318 Chapter 8. Introduction to Nonlinear Models 324 8.1 Introduction 324 8.2 Intrinsically Linear Models 326 8.3 Intrinsically Nonlinear Models 341 8.4 Summary 353 8.5 Chapter Exercises 354 Chapter 9. Indicator Variables 358 9.1 Introduction 358 9.2 The Dummy Variable Model 360 9.3 Unequal Cell Frequencies 367 9.4 Empty Cells 372 9.5 Models with Dummy and Continuous Variables 375 9.6 A Special Application: The Analysis of Covariance 380 9.7 Heterogeneous Slopes in the Analysis of Covariance 384 9.8 Summary 389 9.9 Chapter Exercises 389 Chapter 10. Categorical Response Variables 392 10.1 Introduction 392 10.2 Binary Response Variables 392 10.3 Weighted Least Squares 395 10.4 Simple Logistic Regression 400 10.5 Multiple Logistic Regression 406 10.6 Loglinear Model 409 10.7 Summary 416 10.8 Chapter Exercises 417 Chapter 11. Generalized Linear Models 422 11.1 Introduction 422 11.2 The Link Function 424 11.3 The Logistic Model 425 11.4 Other Models 427 11.5 Summary 431 Appendix A: Statistical Tables 434 A.1 The Standard Normal Distribution—Probabilities Exceeding Z 435 A.2 The T Distribution—Values of T Exceeded with Given Probability 440 A.3 The X2 Distribution—X2 Values Exceeded with Given Probability 441 A.4 The F Distribution p= 0.1 442 A.5 The Durbin–Watson Test Bounds 452 Appendix B: A Brief Introduction Tomatrices 454 B.1 Matrix Algebra 455 B.2 Solving Linear Equations 458 Appendix C: Estimation Procedures 460 C.1 Least Squares Estimation 460 C.2 Maximum Likelihood Estimation 462 References 466 Index 470 0120885972,9780120885978 Academic Press The book provides complete coverage of the classical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design.

* Examples and exercises contain real data and
graphical illustration for ease of interpretation
* Outputs from SAS 7, SPSS 7, Excel, and Minitab are
used for illustration, but any major statistical
software package will work equally well.
* Data sets are furnished on CD included in the text "The book provides complete coverage of the classical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design."--Publisher's website