.

0 (hodnocen0 x )

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BK

3rd ed.

New York : John Wiley & Sons, 1998

xvii,706 s. : il. + 1 disketa

ISBN 0-471-17082-8 (váz.)

Wiley series in mathematical and computational biology

Wiley series in probability and mathematical statistics. Text and references section

Obsahuje grafy, tabulky, předmluvu, rejstříky

Bibliografie: s. 593-603

Analýza regresní - učebnice vysokošk.

000004925

Preface xiii // About the Software xvii // 0 Basic Prerequisite Knowledge 1 // 0.1 Distributions: Normal, t, and F, 1 // 0.2 Confidence Intervals (or Bands) and r-Tests, 4 // 0.3 Elements of Matrix Algebra, 6 // 1 Fitting a Straight Line by Least Squares 15 // 1.0 Introduction: The Need for Statistical Analysis, 15 // 1.1 Straight Line Relationship Between Two Variables, 18 // 1.2 Linear Regression: Fitting a Straight Line by Least Squares, 20 // 1.3 The Analysis of Variance, 28 // 1.4 Confidence Intervals and Tests for ß0 and ßb 34 // 1.5 F-Test for Significance of Regression, 38 // 1.6 The Correlation Between X and ?, 40 // 1.7 Summary of the Straight Line Fit Computations, 44 // 1.8 Historical Remarks, 45 Appendix 1A Steam Plant Data, 46 Exercises are in “Exercises for Chapters 1-3”, 96 // 2 Checking the Straight Line Fit 47 // 2.1 Lack of Fit and Pure Error, 47 // 2.2 Testing Homogeneity of Pure Error, 56 // 2.3 Examining Residuals: The Basic Plots, 59 // 2.4 Non-normality Checks on Residuals, 61 // 2.5 Checks for Time Effects, Nonconstant Variance, Need for Transformation, and Curvature, 62 // 2.6 Other Residuals Plots, 67 // 2.7 Durbin-Watson Test, 69 // 2.8 Reference Books for Analysis of Residuals, 70 Appendix 2A Normal Plots, 70 // Appendix 2B MINITAB Instructions, 76 Exercises are in “Exercises for Chapters 1-3”, 96 // 3 Fitting Straight Lines: Special Topics 79 // 3.0 Summary and Preliminaries, 79 // 3.1 Standard Error of ?, 80 // 3.2 Inverse Regression (Straight Line Case), 83 // 3.3 Some Practical Design of Experiment Implications of Regression, // 86  // 3.4 Straight Line Regression When Both Variables Are Subject to Error, // 89 // Exercises for Chapters 1-3, 96 // 4 Regression in Matrix Terms: Straight Line Case 115 // 4.1 Fitting a Straight Line in Matrix Terms, 115 //

4.2 Singularity: What Happens in Regression to Make X’X Singular? // An Example, 125 // 4.3 The Analysis of Variance in Matrix Terms, 127 // 4.4 The Variances and Covariance of b0 and b] from the Matrix Calculation, 128 // 4.5 Variance of Ý Using the Matrix Development, 130 // 4.6 Summary of Matrix Approach to Fitting a Straight Line (Nonsingular Case), 130 // 4.7 The General Regression Situation, 131 Exercises for Chapter 4, 132 // 5 The General Regression Situation 135 // 5.1 General Linear Regression, 135 // 5.2 Least Squares Properties, 137 // 5.3 Least Squares Properties When e ~ ĚV(0, lo2), 140 // 5.4 Confidence Intervals Versus Regions, 142 // 5.5 More on Confidence Intervals Versus Regions, 143 Appendix 5A Selected Useful Matrix Results, 147 Exercises are in “Exercises for Chapters 5 and 6”, 169 // 6 Extra Sums of Squares and Tests for Several Parameters // Being Zero 149 // 6.1 The “Extra Sum of Squares” Principle, 149 // 6.2 Two Predictor Variables: Example, 154 // 6.3 Sum of Squares of a Set of Linear Functions of T’s, 162 // Appendix 6A Orthogonal Columns in the X Matrix, 165 // Appendix 6B Two Predictors: Sequential Sums of Squares, 167 Exercises for Chapters 5 and 6, 169 // 7 Serial Correlation in the Residuals and the Durbin-Watson Test 179 // 7.1 Serial Correlation in Residuals, 179 // 7.2 The Durbin-Watson Test for a Certain Type of Serial Correlation, 181 // 7.3 Examining Runs in the Time Sequence Plot of Residuals: // Runs Test, 192 // Exercises for Chapter 7, 198 // 8 More on Checking Fitted Models 205 // 8.1 The Hat Matrix H and the Various Types of Residuals, 205 // 8.2 Added Variable Plot and Partial Residuals, 209 // 8.3 Detection of Influential Observations: Cook’s Statistics, 210 // 8.4 Other Statistics Measuring Influence, 214 // 8.5 Reference Books for Analysis of Residuals, 214 Exercises for Chapter 8, 215 //

9 Multiple Regression: Special Topics 217 // 9.1 Testing a General Linear Hypothesis, 217 // 9.2 Generalized Least Squares and Weighted Least Squares, 221 // 9.3 An Example of Weighted Least Squares, 224 // 9.4 A Numerical Example of Weighted Least Squares, 226 // 9.5 Restricted Least Squares, 229 // 9.6 Inverse Regression (Multiple Predictor Case), 229 // 9.7 Planar Regression When All the Variables Are Subject to Error, 231 // Appendix 9A Lagrange’s Undetermined Multipliers, 231 Exercises for Chapter 9, 233 // 10 Bias in Regression Estimates, and Expected Values of Mean // Squares and Sums of Squares 235 // 10.1 Bias in Regression Estimates, 235 // 10.2 The Effect of Bias on the Least Squares Analysis of Variance, 238 // 10.3 Finding the Expected Values of Mean Squares, 239 // 10.4 Expected Value of Extra Sum of Squares, 240 Exercises for Chapter 10, 241 // 11 On Worthwhile Regressions, Big F’s, and R2 243 // 11.1 Is My Regression a Useful One?, 243 // 11.2 A Conversation About R2, 245 // Appendix ?? How Significant Should My Regression Be?, 247 Exercises for Chapter 11, 250 // 12 Models Containing Functions of the Predictors, Including Polynomial Models // 12.1 More Complicated Model Functions, 251 // 12.2 Worked Examples of Second-Order Surface Fitting for ? ? = 2 Predictor Variables, 254 // 12.3 Retaining Terms in Polynomial Models, 266 Exercises for Chapter 12, 272 // 13 Transformation of the Response Variable 277 // 13.1 Introduction and Preliminary Remarks, 277 // 13.2 Power Family of Transformations on the Response: Box-Cox Method, 280 // 13.3 A Second Method for Estimation A, 286 // 13.4 Response Transformations: Other Interesting and Sometimes Useful Plots, 289 // 13.5 Other Types of Response Transformations, 290 // 13.6 Response Transformations Chosen to Stabilize Variance, 291 Exercises for Chapter 13, 294 //

14 "Dummy" Variables 299 // 14.1 Dummy Variables to Separate Blocks of Data with Different Intercepts, Same Model, 299 // 14.2 Interaction Terms Involving Dummy Variables, 307 // 14.3 Dummy Variables for Segmented Models, 311 Exercises for Chapter 14, 317 // 15 Selecting the "Best" Regression Equation 327 // 15.0 Introduction, 327 // 15.1 All Possible Regressions and “Best Subset” Regression, 329 // 15.2 Stepwise Regression, 335 // 15.3 Backward Elimination, 339 // 15.4 Significance Levels for Selection Procedures, 342 // 15.5 Variations and Summary, 343 // 15.6 Selection Procedures Applied to the Steam Data, 345 // Appendix 15A Hald Data, Correlation Matrix, and All 15 Possible Regressions, 348 Exercises for Chapter 15, 355 // 16 Ill-Conditioning in Regression Data 369 // 16.1 Introduction, 369 // 16.2 Centering Regression Data, 371 // 16.3 Centering and Scaling Regression Data, 373 // 16.4 Measuring Multicollinearity, 375 // 16.5 Belsley’s Suggestion for Detecting Multicollinearity, 376 Appendix 16A Transforming X Matrices to Obtain Orthogonal // Columns, 382 // Exercises for Chapter 16, 385 // 17 Ridge Regression 387 // 17.1 Introduction, 387 // 17.2 Basic Form of Ridge Regression, 387 // 17.3 Ridge Regression of the Hald Data, 389 // 17.4 In What Circumstances Is Ridge Regression Absolutely the Correct Way to Proceed?, 391 // 17.5 The Phoney Data Viewpoint, 394 // 17.6 Concluding Remarks, 395 // Appendix 17A Ridge Estimates in Terms of Least Squares Estimates, // 396 // Appendix 17B Mean Square Error Argument, 396 Appendix 17C Canonical Form of Ridge Regression, 397 Exercises for Chapter 17, 400 // 18 Generalized Linear Models (GLIM) 401 // 18.1 Introduction, 401 // 18.2 The Exponential Family of Distributions, 402 // 18.3 Fitting Generalized Linear Models (GLIM), 404 // 18.4 Performing the Calculations: An Example, 406 // 18.5 Further Reading, 408 // Exercices for the Chapter 18, 408 //

19 Mixture Ingredients as Predictor Variables 409 // 19.1 Mixture Experiments: Experimental Spaces, 409 // 19.2 Models for Mixture Experiments, 412 // 19.3 Mixture Experiments in Restricted Regions, 416 // 19.4 Example 1, 418 // 19.5 Example 2, 419 // Appendix 19A Transforming ? Mixture Variables to — 1 Working Variables, 422 // Exercises for Chapter 19, 425 // 20 The Geometry of Least Squares 427 // 20.1 The Basic Geometry, 427 // 20.2 Pythagoras and Analysis of Variance, 429 // 20.3 Analysis of Variance and F-Test for Overall Regression, 432 // 20.4 The Singular X’X Case: An Example, 433 // 20.5 Orthogonalizing in the General Regression Case, 435 // 20.6 Range Space and Null Space of a Matrix M, 437 // 20.7 The Algebra and Geometry of Pure Error, 439 Appendix 20A Generalized Inverses M , 441 Exercises for Chapter 20, 444 // 21 More Geometry of Least Squares 447 // 21.1 The Geometry of a Null Hypothesis: A Simple Example, 447 // 21.2 General Case Ho . Aß = c: The Projection Algebra, 448 // 21.3 Geometric Illustrations, 449 // 21.4 The F-Test for ?0, Geometrically, 450 // 21.5 The Geometry of F2, 452 // 21.6 Change in R2 for Models Nested Via Aß = 0, Not Involving ?? // 452 U " // 21.7 Multiple Regression with Two Predictor Variables as a Sequence of Straight Line Regressions, 454 // Exercises for Chapter 21, 459 // 22 Orthogonal Polynomials and Summary Data 461 // 22.1 Introduction, 461 // 22.2 Orthogonal Polynomials, 461 // 22.3 Regression Analysis of Summary Data, 467 Exercises for Chapter 22, 469 // 23 Multiple Regression Applied to Analysis of Variance Problems 473 // 23.1 Introduction, 473 // 23.2 The One-Way Classification: Standard Analysis and an Example, 474 // 23.3 Regression Treatment of the One-Way Classification Example, 477 // 23.4 Regression Treatment of the One-Way Classification Using the Original Model, 481 //

23.5 Regression Treatment of the One-Way Classification: Independent Normal Equations, 486 // 23.6 The Two-Way Classification with Equal Numbers of Observations in the Cells: An Example, 488 // 23.7 Regression Treatment of the Two-Way Classification Example, 489 // 23.8 The Two-Way Classification with Equal Numbers of Observations in the Cells, 493 // 23.9 Regression Treatment of the Two-Way Classification with Equal Numbers of Observations in the Cells, 494 // 23.10 Example: The Two-Way Classification, 498 // 23.11 Recapitulation and Comments, 499 Exercises for Chapter 23, 500 // 24 An Introduction to Nonlinear Estimation 505 // 24.1 Least Squares for Nonlinear Models, 505 // 24.2 Estimating the Parameters of a Nonlinear System, 508 // 24.3 An Example, 518 // 24.4 A Note on Reparameterization of the Model, 529 // 24.5 The Geometry of Linear Least Squares, 530 // 24.6 The Geometry of Nonlinear Least Squares, 539 // 24.7 Nonlinear Growth Models, 543 // 24.8 Nonlinear Models: Other Work, 550 // 24.9 References, 553 // Exercises for Chapter 24, 553 // 25 Robust Regression 567 // 25.1 Least Absolute Deviations Regression (Lj Regression), 567 // 25.2 M-Estimators, 567 // 25.3 Steel Employment Example, 573 // 25.4 Trees Example, 575 // 25.5 Least Median of Squares (LMS) Regression, 577 // 25.6 Robust Regression with Ranked Residuals (rreg), 577 // 25.7 Other Methods, 580 // 25.8 Comments and Opinions, 580 // 25.9 References, 581 Exercises for Chapter 25, 584 // 26 Resampling Procedures (Bootstrapping) 585 // 26.1 Resampling Procedures for Regression Models, 585 // 26.2 Example: Straight Line Fit, 586 // 26.3 Example: Planar Fit, Three Predictors, 588 // 26.4 Reference Books, 588 // Appendix 26A Sample MINITAB Programs to Bootstrap Residuals for a Specific Example, 589 // Appendix 26B Sample MINITAB Programs to Bootstrap Pairs for a Specific Example, 590 //

Additional Comments, 591 Exercises for Chapter 26, 591 // Bibliography 593 // True/False Questions 605 // Answers to Exercises 609 // Tables // Normal Distribution, 684 Percentage Points of the /-Distribution, 686 Percentage Points of the Distribution, 687 // Percentage Points of the  -Distribution, 688 // Index of Authors Associated with Exercises