Regression Analysis: Concepts and Applications

Preface......Page 5
Contents......Page 14
1.1 Overview......Page 18
1.2 Basic Ingredients for Statistical Inference......Page 20
1.3 Population......Page 22
1.4 Model......Page 27
1.5 Parameters(Summary Numbers)......Page 31
1.6 Samples and Inferences......Page 37
1.7 Function Notation......Page 64
1.8 Matrices and Vectors......Page 67
1.9 Multivariate Gaussian Populations......Page 79
1.10 Exercises......Page 87
2.2 Prediction......Page 90
2.3 Regression Analysis......Page 99
2.4 Exercises......Page 114
3.1 Overview......Page 116
3.2 An example of Straight Line Regression......Page 117
3.3 Straight Line Regression Model-Assumptions (A) and (B)......Page 126
3.4 Point Estimation......Page 129
3.5 Checking Assumptions......Page 149
3.6 Confidence Intervals......Page 178
3.7 Tests......Page 188
3.8 Analysis of Variance......Page 195
3.9 Coefficient of Determination and Coefficient Correlation......Page 198
3.10 Regression Analysis When There Are Measurement Errors......Page 211
3.11 Regression Through the Origin......Page 227
3.12 Exercises......Page 231
4.1 Overview......Page 236
4.2 Notation and Definitions......Page 237
4.3 Assumptions for Multiple Linear Regression......Page 249
4.4 Point Estimation......Page 252
4.5 Residual Analysis......Page 268
4.6 Confidence Intervals......Page 279
4.7 Tests......Page 295
4.8 Analysis of Variance......Page 300
4.9 Comparison of Two Regression Function and Coefficients of Determination......Page 308
4.10 Comparing Two Multiple Regression Models(Nonnested Case)......Page 326
4.11 Lack-of-Fit Analysis......Page 335
4.12 Exercises......Page 353
5.1 Overview......Page 369
5.2 Outliers......Page 370
5.3 Leverages Hat Values......Page 383
5.4 Influential Observations-Cook's Distance and DFFITS......Page 389
5.5 III-Conditioning and Multicollinearity......Page 410
5.6 Exercises......Page 417
6.2 Prediction Intervals......Page 420
6.3 Tolerance Intervals......Page 433
6.4 Calibration and Regulation for Straight Line Regression......Page 442
6.5 Comparison of Serval Straight Line Regressions-Identical, Parallel, and Intersecting Lines......Page 453
6.6 Intersection of Two Straight Line Regression Function......Page 467
6.7 Maximum or Minimum of a Quadratic Regression Model......Page 473
6.8 Linear Splines......Page 482
6.9 Exercises......Page 493
7.2 Subset Analysis and Variable Selection......Page 518
7.3 All-Subsets Regression......Page 521
7.4 Alternative Methods for Subset Selection......Page 537
7.5 Growth Curves......Page 568
7.6 Exercises......Page 584
8.2 Straight Line Regression with Unequal Subpopulation Standard Deviations......Page 588
8.3 Straight Line Regression-Theil's Method......Page 601
8.4 Exercises......Page 609
9.2 Some Commonly Used Families of Nonlinear Regression Functions......Page 616
9.3 Statistical Assumptions and Inferences for Nonlinear Regression......Page 622
9.4 Linearizable Models......Page 632
9.5 Exercises......Page 639
Index for Data Sets......Page 644
Index......Page 645