Applied regression analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1981
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in probability and mathematical statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 709 S. graph. Darst. |
| ISBN: | 0471029955 |
Internformat
MARC
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| 245 | 1 | 0 | |a Applied regression analysis |c N. R. Draper ; H. Smith |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1981 | |
| 300 | |a XIV, 709 S. |b graph. Darst. | ||
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| 490 | 0 | |a Wiley series in probability and mathematical statistics | |
| 650 | 7 | |a Regression Analysis |2 cabt | |
| 650 | 4 | |a Analyse de régression | |
| 650 | 7 | |a Regressieanalyse |2 gtt | |
| 650 | 7 | |a Régression, analyse de |2 ram | |
| 650 | 4 | |a Regression analysis | |
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Datensatz im Suchindex
| _version_ | 1804116445437624320 |
|---|---|
| adam_text | Contents
chapter page
1 Fitting a Straight Line by Least Squares 1
1.0 Introduction: The Need for Statistical Analysis .... 1
1.1 Straight Line Relationships between Two Variables ... 5
1.2 Linear Regression: Fitting a Straight Line ..... 8
1.3 The Precision of the Estimated Regression . . . . .17
1.4 Examining the Regression Equation ...... 22
1.5 Lack of Fit and Pure Error 33
1.6 The Correlation between X and Y 43
1.7 Inverse Regression (Straight Line Case) ..... 47
1.8 Some Practical Implications of Chapter 1 . . . . .51
Exercises ........... 55
2 The Matrix Approach to Linear Regression . . . .70
2.0 Introduction 70
2.1 Fitting a Straight Line in Matrix Terms: The Estimates of fla and /?, 70
2.2 The Analysis of Variance in Matrix Terms ..... 80
2.3 The Variances and Covariance of b0 and ft, from the
Matrix Calculation 82
2.4 Variance of Y Using the Matrix Development . . . .83
2.5 Summary of Matrix Approach to Fitting a Straight Line . . 84
2.6 The General Regression Situation ...... 85
2.7 The Extra Sum of Squares Principle 97
2.8 Orthogonal Columns in the Jf Matrix 98
2.9 Partial F Tests and Sequential F Tests 101
2.10 Testing a General Linear Hypothesis in Regression Situations . .102
2.11 Weighted Least Squares 108
2.12 Bias in Regression Estimates . . . . . . .117
2.13 Restricted Least Squares 122
2.14 Some Notes on Errors in the Predictors (As Well as in
the Response) 122
2.15 Inverse Regression (Multiple Predictor Case) 125
Appendix 2A Selected Useful Matrix Results . . . .126
Appendix 2B Expected Value of Extra Sum of Squares . . .128
xi
xii CONTENTS
Appendix 2C How Significant Should My Regression Be? . .129
Appendix 2D Lagrange s Undetermined Multipliers . . .134
Exercises . . . . . . ¦ . . . .136
3 The Examination of Residuals 141
3.0 Introduction 141
3.1 Overall Plot 142
3.2 Time Sequence Plot ......... 145
3.3 Plot Against % ... 147
3.4 Plot Against the Predictor Variables Xy,, i= 1, 2, ... ,« . . 148
3.5 Other Residuals Plots 149
3.6 Statistics for Examination of Residuals . . . . . 150
3.7 Correlations among the Residuals ...... 151
3.8 Outliers 152
3.9 Serial Correlation in Residuals .153
3.10 Examining Runs in the Time Sequence Plot of Residuals . . 157
3.11 The Durbin Watson Test for a Certain Type of Serial Correlation . 162
3.12 Detection of Influential Observations . . . . . .169
Appendix 3A. Normal and Half Normal Plots . . . .177
Exercises ........... 183
4 Two Predictor Variables 193
4.0 Introduction 193
4.1 Multiple Regression with Two Predictor Variables as a
Sequence of Straight Line Regressions . . . . . .196
4.2 Examining the Regression Equation ...... 204
Exercises ........... 212
5 More Complicated Models 218
5.0 Introduction 218
5.1 Polynomial Models of Various Orders in the Xs . . . .219
5.2 Models Involving Transformations Other Than Integer Powers . 221
5.3 Families of Transformations ....... 225
5.4 The Use of Dummy Variables in Multiple Regression . . . 241
5.5 Centering and Scaling; Performing the Regression in Correlation Form 257
5.6 Orthogonal Polynomials ........ 266
5.7 Transforming X Matrices to Obtain Orthogonal Columns . . 275
5.8 Regression Analysis of Summary Data ...... 278
Exercises ........... 280
CONTENTS xiii
6 Selecting the Best Regression Equation .... 294
6.0 Introduction 294
6.1 All Possible Regressions 296
6.2 Best Subset Regression 303
6.3 The Backward Elimination Procedure ...... 305
6.4 The Stepwise Regression Procedure ...... 307
6.5 A Drawback to Understand but not be Overly Concerned About . 311
6.6 Variations on the Previous Methods . . . . . .312
6.7 Ridge Regression . . . . . . . . .313
6.8 PRESS 325
6.9 Principal Component Regression ....... 327
6.10 Latent Root Regression 332
6.11 The Stagewise Regression Procedure ...... 337
6.12 Summary 341
6.13 Computational Method for Stepwise Regression .... 342
6.14 Robust Regression 342
6.15 Some Comments on Statistical Computer Packages . . . 344
Appendix 6A Canonical Form of Ridge Regression . . . 349
Exercises ........... 352
7 Two Specific Problems 380
7.0 Introduction 380
7.1 The First Problem 380
7.2 Examination of the Data 381
7.3 Choosing the First Variable to Enter Regression .... 383
7.4 Construction of New Variables ....... 386
7.5 The Addition of a Cross Product Term to the Model . . . 386
7.6 Enlarging the Model 388
7.7 The Second Problem. Worked Examples of Second Order
Surface Fitting for k = 3 and k = 2 Variables . . . .390
Exercises ........... 404
8 Multiple Regression and Mathematical Model Building 412
8.0 Introduction 412
8.1 Planning the Model Building Process ...... 414
8.2 Development of the Mathematical Model ..... 418
8.3 Validation and Maintenance of the Mathematical Model . . 419
9 Multiple Regression Applied to Analysis of
Variance Problems 423
9.0 Introduction 423
9.1 TheOne Way Classification: An Example 424
9.2 Regression Treatment of the One Way Classification Example . . 427
xiv CONTENTS
9.3 The One Way Classification 431
9.4 Regression Treatment of the One Way Classification
Using the Original Model ........ 432
9.5 Regression Treatment of the One Way Classification:
Independent Normal Equations ....... 437
9.6 The Two Way Classification with Equal Numbers of
Observations in the Cells: An Example ..... 439
9.7 Regression Treatment of the Two Way Classification Example. . 441
9.8 The Two Way Classification with Equal Numbers of
Observations in the Cells ........ 445
9.9 Regression Treatment of the Two Way Classification
with Equal Numbers of Observations in the Cells .... 447
9.10 Example: The Two Way Classification . . . . . .451
9.11 Comments 453
Exercises ........... 454
10 An Introduction to Nonlinear Estimation .... 458
10.0 Introduction 458
10.1 Least Squares in the Nonlinear Case ...... 459
10.2 Estimating the Parameters of a Nonlinear System .... 462
10.3 An Example 475
10.4 A Note on Reparameterization of the Model . .... 488
10.5 The Geometry of Linear Least Squares . ..... 489
10.6 The Geometry of Nonlinear Least Squares ..... 500
10.7 Nonlinear Growth Models 505
10.8 Nonlinear Models: Other Work 513
Exercises ........... 517
Normal Distribution 530
Percentage Points of the ^ Distribution 532
Percentage Points of the F Distribution 533
Answers to Exercises 537
Appendix A 611
Appendix B 629
Appendix C 661
Bibliography 675
Index 701
|
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| author | Draper, Norman Richard 1931- Smith, Harry |
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| bvnumber | BV001998130 |
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| dewey-full | 519.5/36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/36 |
| dewey-search | 519.5/36 |
| dewey-sort | 3519.5 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Politologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| isbn | 0471029955 |
| language | English |
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| publishDate | 1981 |
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| spelling | Draper, Norman Richard 1931- Verfasser (DE-588)108415074 aut Applied regression analysis N. R. Draper ; H. Smith 2. ed. New York [u.a.] Wiley 1981 XIV, 709 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Regression Analysis cabt Analyse de régression Regressieanalyse gtt Régression, analyse de ram Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s DE-604 Anwendung (DE-588)4196864-5 s Smith, Harry Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Draper, Norman Richard 1931- Smith, Harry Applied regression analysis Regression Analysis cabt Analyse de régression Regressieanalyse gtt Régression, analyse de ram Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Anwendung (DE-588)4196864-5 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4196864-5 |
| title | Applied regression analysis |
| title_auth | Applied regression analysis |
| title_exact_search | Applied regression analysis |
| title_full | Applied regression analysis N. R. Draper ; H. Smith |
| title_fullStr | Applied regression analysis N. R. Draper ; H. Smith |
| title_full_unstemmed | Applied regression analysis N. R. Draper ; H. Smith |
| title_short | Applied regression analysis |
| title_sort | applied regression analysis |
| topic | Regression Analysis cabt Analyse de régression Regressieanalyse gtt Régression, analyse de ram Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Anwendung (DE-588)4196864-5 gnd |
| topic_facet | Regression Analysis Analyse de régression Regressieanalyse Régression, analyse de Regression analysis Regressionsanalyse Anwendung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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