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
Author(s): Rudolf J. Freund, William J. Wilson, Ping Sa
Edition: 2
Publisher: Academic Press
Year: 2006
Language: English
Pages: 480
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;
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
