Applied regression analysis:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1998
|
| Edition: | 3. ed. |
| Series: | Wiley series in probability and statistics : Texts and references section
|
| Subjects: | |
| Online Access: | Publisher description Table of Contents Inhaltsverzeichnis |
| Physical Description: | XVII, 706 S. graph. Darst. 1 Diskette (9 cm) |
| ISBN: | 0471170828 9780471170822 |
Staff View
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Record in the Search Index
| _version_ | 1804126606405402624 |
|---|---|
| adam_text | Contents
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 f 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 /3n and /3,, 34
1.5 F Test for Significance of Regression, 38
1.6 The Correlation Between X and 7, 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
v
Vi CONTENTS
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 Y, 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 bx from the Matrix
Calculation, 128
4.5 Variance of Y 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 ~ N(0, la2), 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 F s, 162
CONTENTS VM
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 Conversion About R 245
ViM CONTENTS
Appendix 11A How Significant Should My Regression Be?, 247
Exercises for Chapter 11, 250
12 Models Containing Functions of the Predictors, Including
Polynomial Models 251
12.1 More Complicated Model Functions, 251
12.2 Worked Examples of Second Order Surface Fitting for k = 3 and
k = 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
CONTENTS JX
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
Exercises for 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 k Mixture Variables to k 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
X CONTENTS
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 H0:A(J = c: The Projection Algebra, 448
21.3 Geometric Illustrations, 449
21.4 The F Test for Ho, Geometrically, 450
21.5 The Geometry of R2, 452
21.6 Change in R2 for Models Nested Via A/3 = 0, Not Involving /30,
452
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
CONTENTS XJ
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 (L, 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
Xii CONTENTS
Tables 684
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 695
Index 697
|
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| dewey-sort | 3519.5 236 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-09T18:20:08Z |
| institution | BVB |
| isbn | 0471170828 9780471170822 |
| language | English |
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| spelling | Draper, Norman Richard 1931- Verfasser (DE-588)108415074 aut Applied regression analysis Norman R. Draper ; Harry Smith 3. ed. New York [u.a.] Wiley 1998 XVII, 706 S. graph. Darst. 1 Diskette (9 cm) txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics : Texts and references section Regression analysis Anwendung (DE-588)4196864-5 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Anwendung (DE-588)4196864-5 s 1\p DE-604 Smith, Harry Verfasser aut http://www.loc.gov/catdir/description/wiley033/97017969.html Publisher description http://www.loc.gov/catdir/toc/onix04/97017969.html Table of Contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008127661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Draper, Norman Richard 1931- Smith, Harry Applied regression analysis Regression analysis Anwendung (DE-588)4196864-5 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4129903-6 |
| title | Applied regression analysis |
| title_auth | Applied regression analysis |
| title_exact_search | Applied regression analysis |
| title_full | Applied regression analysis Norman R. Draper ; Harry Smith |
| title_fullStr | Applied regression analysis Norman R. Draper ; Harry Smith |
| title_full_unstemmed | Applied regression analysis Norman R. Draper ; Harry Smith |
| title_short | Applied regression analysis |
| title_sort | applied regression analysis |
| topic | Regression analysis Anwendung (DE-588)4196864-5 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Regression analysis Anwendung Regressionsanalyse |
| url | http://www.loc.gov/catdir/description/wiley033/97017969.html http://www.loc.gov/catdir/toc/onix04/97017969.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008127661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT drapernormanrichard appliedregressionanalysis AT smithharry appliedregressionanalysis |