Introduction to linear regression analysis:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2001
|
| Edition: | 3. ed. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Publisher description Table of Contents Inhaltsverzeichnis |
| Item Description: | Erg. bildet: Montgomery, Douglas C.: Student solutions manual to accompany Introduction to linear regression analysis |
| Physical Description: | XVI, 641 S. graph. Darst. |
| ISBN: | 0471315656 |
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| adam_text | INTRODUCTION TO LINEAR REGRESSION ANALYSIS * ~ * * * - - * * . . . . .
. . . . . . . . . . THIRD EDITION J * * ! ^ ; DOUGLAS C. MONTGOMERY
ARIZONA STATE UNIVERSITY ELIZABETH A. PECK THE COCA-COLA COMPANY G.
GEOFFREY VINING VIRGINIA TECH A WILEY INTERSCIENCE PUBLICATION JOHN
WILEY & SONS, INC. NEW YORK * CHICHESTER * WEINHEIM * BRISBANE *
SINGAPORE * TORONTO CONTENTS PREFACE XIII 1. INTRODUCTION 1 1.1
REGRESSION AND MODEL BUILDING, 1 1.2 DATA COLLECTION, 7 1.3 USES OF
REGRESSION, 11 1.4 ROLE OF THE COMPUTER, 12 2. SIMPLE LINEAR REGRESSION
13 2.1 SIMPLE LINEAR REGRESSION MODEL, 13 2.2 LEAST-SQUARES ESTIMATION
OF THE PARAMETERS, 14 2.2.1 ESTIMATION OF /3 0 AND /?,, 14 2.2.2
PROPERTIES OF THE LEAST-SQUARES ESTIMATORS AND THE FITTED REGRESSION
MODEL, 20 2.2.3 ESTIMATION OF A 2 , 22 2.2.4 AN ALTERNATE FORM OF THE
MODEL, 24 2.3 HYPOTHESIS TESTING ON THE SLOPE AND INTERCEPT, 24 2.3.1
USE OF /-TESTS, 25 2.3.2 TESTING SIGNIFICANCE OF REGRESSION, 26 2.3.3
THE ANALYSIS OF VARIANCE, 28 2.4 INTERVAL ESTIMATION IN SIMPLE LINEAR
REGRESSION, 32 2.4.1 CONFIDENCE INTERVALS ON /3 0 , /3,, AND A 2 , 32
2.4.2 INTERVAL ESTIMATION OF THE MEAN RESPONSE, 34 2.5 PREDICTION OF NEW
OBSERVATIONS, 37 2.6 COEFFICIENT OF DETERMINATION, 39 2.7 SOME
CONSIDERATIONS IN THE USE OF REGRESSION, 41 2.8 REGRESSION THROUGH THE
ORIGIN, 44 VI CONTENTS 2.9 ESTIMATION BY MAXIMUM LIKELIHOOD, 50 2.10
CASE WHERE THE REGRESSOR X IS RANDOM, 52 2.10.1 X AND Y JOINTLY
DISTRIBUTED, 52 2.10.2 X AND Y JOINTLY NORMALLY DISTRIBUTED: THE
CORRELATION MODEL, 53 PROBLEMS, 58 3. MULTIPLE LINEAR REGRESSION 67 3.1
MULTIPLE REGRESSION MODELS, 67 3.2 ESTIMATION OF THE MODEL PARAMETERS,
71 3.2.1 LEAST-SQUARES ESTIMATION OF THE REGRESSION COEFFICIENTS, 71
3.2.2 A GEOMETRICAL INTERPRETATION OF LEAST SQUARES, 81 3.2.3 PROPERTIES
OF THE LEAST-SQUARES ESTIMATORS, 82 3.2.4 ESTIMATION OF A 2 , 82 3.2.5
INADEQUACY OF SCATTER DIAGRAMS IN MULTIPLE REGRESSION, 84 3.2.6
MAXIMUM-LIKELIHOOD ESTIMATION, 85 3.3 HYPOTHESIS TESTING IN MULTIPLE
LINEAR REGRESSION, 87 3.3.1 TEST FOR SIGNIFICANCE OF REGRESSION, 87
3.3.2 TESTS ON INDIVIDUAL REGRESSION COEFFICIENTS, 91 3.3.3 SPECIAL CASE
OF ORTHOGONAL COLUMNS IN X, 96 3.3.4 TESTING THE GENERAL LINEAR
HYPOTHESIS, 98 3.4 CONFIDENCE INTERVALS IN MULTIPLE REGRESSION, 101
3.4.1 CONFIDENCE INTERVALS ON THE REGRESSION COEFFICIENTS, 102 3.4.2
CONFIDENCE INTERVAL ESTIMATION OF THE MEAN RESPONSE, 103 3.4.3
SIMULTANEOUS CONFIDENCE INTERVALS ON REGRESSION COEFFICIENTS, 104 3.5
PREDICTION OF NEW OBSERVATIONS, 108 3.6 HIDDEN EXTRAPOLATION IN MULTIPLE
REGRESSION, 109 3.7 STANDARDIZED REGRESSION COEFFICIENTS, 112 3.8
MULTICOLLINEARITY, 117 3.9 WHY DO REGRESSION COEFFICIENTS HAVE THE WRONG
SIGN?, 120 PROBLEMS, 122 CONTENTS VII 4. MODEL ADEQUACY CHECKING 131 4.1
INTRODUCTION, 131 4.2 RESIDUAL ANALYSIS, 132 4.2.1 DEFINITION OF
RESIDUALS, 132 4.2.2 METHODS FOR SCALING RESIDUALS, 132 4.2.3 RESIDUAL
PLOTS, 138 4.2.4 PARTIAL REGRESSION AND PARTIAL RESIDUAL PLOTS, 146
4.2.5 OTHER RESIDUAL PLOTTING AND ANALYSIS METHODS, 150 4.3 THE PRESS
STATISTIC, 152 4.4 DETECTION AND TREATMENT OF OUTLIERS, 154 4.5 LACK OF
FIT OF THE REGRESSION MODEL, 158 4.5.1 A FORMAL TEST FOR LACK OF FIT,
158 4.5.2 ESTIMATION OF PURE ERROR FROM NEAR-NEIGHBORS, 162 PROBLEMS,
166 5. TRANSFORMATIONS AND WEIGHTING TO CORRECT MODEL INADEQUACIES 173
5.1 INTRODUCTION, 173 5.2 VARIANCE-STABILIZING TRANSFORMATIONS, 174 5.3
TRANSFORMATIONS TO LINEARIZE THE MODEL, 178 5.4 ANALYTICAL METHODS FOR
SELECTING A TRANSFORMATION, 186 5.4.1 TRANSFORMATIONS ON Y: THE BOX-COX
METHOD, 186 5.4.2 TRANSFORMATIONS ON THE REGRESSOR VARIABLES, 189 5.5
GENERALIZED AND WEIGHTED LEAST SQUARES, 193 5.5.1 GENERALIZED LEAST
SQUARES, 193 5.5.2 WEIGHTED LEAST SQUARES, 195 5.5.3 SOME PRACTICAL
ISSUES, 196 PROBLEMS, 200 6. DIAGNOSTICS FOR LEVERAGE AND INFLUENCE 207
6.1 IMPORTANCE OF DETECTING INFLUENTIAL OBSERVATIONS, 207 6.2 LEVERAGE,
209 6.3 MEASURES OF INFLUENCE: COOK S D, 210 6.4 MEASURES OF INFLUENCE:
DFFITS AND DFBETAS, 213 6.5 A MEASURE OF MODEL PERFORMANCE, 216 6.6
DETECTING GROUPS OF INFLUENTIAL OBSERVATIONS, 217 VIII CONTENTS 6.7
TREATMENT OF INFLUENTIAL OBSERVATIONS, 218 PROBLEMS, 219 7. POLYNOMIAL
REGRESSION MODELS 221 7.1 INTRODUCTION, 221 7.2 POLYNOMIAL MODELS IN ONE
VARIABLE, 221 7.2.1 BASIC PRINCIPLES, 221 7.2.2 PIECEWISE POLYNOMIAL
FITTING (SPLINES), 228 7.2.3 POLYNOMIAL AND TRIGONOMETRIC TERMS, 236 7.3
NONPARAMETRIC REGRESSION, 237 7.3.1 KERNEL REGRESSION, 238 7.3.2 LOCALLY
WEIGHTED REGRESSION (LOESS), 239 7.3.3 FINAL CAUTIONS, 243 7.4
POLYNOMIAL MODELS IN TWO OR MORE VARIABLES, 244 7.5 ORTHOGONAL
POLYNOMIALS, 253 PROBLEMS, 258 8. INDICATOR VARIABLES 265 8.1 THE
GENERAL CONCEPT OF INDICATOR VARIABLES, 265 8.2 COMMENTS ON THE USE OF
INDICATOR VARIABLES, 279 8.2.1 INDICATOR VARIABLES VERSUS REGRESSION ON
ALLOCATED CODES, 279 8.2.2 INDICATOR VARIABLES AS A SUBSTITUTE FOR A
QUANTITATIVE REGRESSOR, 280 8.3 REGRESSION APPROACH TO ANALYSIS OF
VARIANCE, 281 PROBLEMS, 287 9. VARIABLE SELECTION AND MODEL BUILDING 291
9.1 INTRODUCTION, 291 9.1.1 THE MODEL-BUILDING PROBLEM, 291 9.1.2
CONSEQUENCES OF MODEL MISSPECIFICATION, 292 9.1.3 CRITERIA FOR
EVALUATING SUBSET REGRESSION MODELS, 296 9.2 COMPUTATIONAL TECHNIQUES
FOR VARIABLE SELECTION, 302 9.2.1 ALL POSSIBLE REGRESSIONS, 302 9.2.2
STEPWISE REGRESSION METHODS, 310 9.3 SOME FINAL RECOMMENDATIONS FOR
PRACTICE, 317 PROBLEMS, 318 CONTENTS IX 10. MULTICOLLINEARITY 325 10.1
INTRODUCTION, 325 10.2 SOURCES OF MULTICOLLINEARITY, 325 10.3 EFFECTS OF
MULTICOLLINEARITY, 328 10.4 MULTICOLLINEARITY DIAGNOSTICS, 334 10.4.1
EXAMINATION OF THE CORRELATION MATRIX, 334 10.4.2 VARIANCE INFLATION
FACTORS, 337 10.4.3 EIGENSYSTEM ANALYSIS OF X X, 339 10.4.4 OTHER
DIAGNOSTICS, 343 10.5 METHODS FOR DEALING WITH MULTICOLLINEARITY, 345
10.5.1 COLLECTING ADDITIONAL DATA, 345 10.5.2 MODEL RESPECIFICATION, 346
10.5.3 RIDGE REGRESSION, 348 10.5.4 OTHER METHODS, 363 10.5.5 COMPARISON
AND EVALUATION OF BIASED ESTIMATORS, 375 PROBLEMS, 378 11. ROBUST
REGRESSION 382 11.1 THE NEED FOR ROBUST REGRESSION, 382 11.2
M-ESTIMATORS, 386 11.3 PROPERTIES OF ROBUST ESTIMATORS, 400 11.3.1
BREAKDOWN POINT, 400 11.3.2 EFFICIENCY, 401 11.4 SURVEY OF OTHER ROBUST
REGRESSION ESTIMATORS, 401 11.4.1 HIGH-BREAKDOWN-POINT ESTIMATORS, 401
11.4.2 BOUNDED INFLUENCE ESTIMATORS, 406 11.4.3 OTHER PROCEDURES, 407
11.4.4 COMPUTING ROBUST REGRESSION ESTIMATORS, 409 PROBLEMS, 410 12.
INTRODUCTION TO NONLINEAR REGRESSION 414 12.1 LINEAR AND NONLINEAR
REGRESSION MODELS, 414 12.1.1 LINEAR REGRESSION MODELS, 414 12.1.2
NONLINEAR REGRESSION MODELS, 415 12.2 NONLINEAR LEAST SQUARES, 416 12.3
TRANSFORMATION TO A LINEAR MODEL, 420 X CONTENTS 12.4 PARAMETER
ESTIMATION IN A NONLINEAR SYSTEM, 423 12.4.1 LINEARIZATION, 423 12.4.2
OTHER PARAMETER ESTIMATION METHODS, 431 12.4.3 STARTING VALUES, 432
12.4.4 COMPUTER PROGRAMS, 433 12.5 STATISTICAL INFERENCE IN NONLINEAR
REGRESSION, 434 12.6 EXAMPLES OF NONLINEAR REGRESSION MODELS, 437
PROBLEMS, 438 13. GENERALIZED LINEAR MODELS 443 13.1 INTRODUCTION, 443
13.2 LOGISTIC REGRESSION MODELS, 444 13.2.1 MODELS WITH A BINARY
RESPONSE VARIABLE, 444 13.2.2 ESTIMATING THE PARAMETERS IN A LOGISTIC
REGRESSION MODEL, 447 13.2.3 INTERPRETATION OF THE PARAMETERS IN A
LOGISTIC REGRESSION MODEL, 450 13.2.4 HYPOTHESIS TESTS ON MODEL
PARAM6TERS, 453 13.3 POISSON REGRESSION, 459 13.4 THE GENERALIZED LINEAR
MODEL, 466 13.4.1 LINK FUNCTIONS AND LINEAR PREDICTORS, 467 13.4.2
PARAMETER ESTIMATION AND INFERENCE IN THE GLM, 468 13.4.3 PREDICTION AND
ESTIMATION WITH THE GLM, 472 13.4.4 RESIDUAL ANALYSIS IN THE GLM, 474
13.4.5 OVERDISPERSION, 475 PROBLEMS, 477 14. OTHER TOPICS IN THE USE OF
REGRESSION ANALYSIS * 488 14.1 REGRESSION MODELS WITH AUTOCORRELATION
ERRORS, 488 14.1.1 SOURCE AND EFFECTS OF AUTOCORRELATION, 488 14.1.2
DETECTING THE PRESENCE OF AUTOCORRELATION, 489 14.1.3 PARAMETER
ESTIMATION METHODS, 494 14.2 EFFECT OF MEASUREMENT ERRORS IN THE
REGRESSORS, 500 14.2.1 SIMPLE LINEAR REGRESSION, 501 14.2.2 THE BERKSON
MODEL, 502 14.3 INVERSE ESTIMATION*THE CALIBRATION PROBLEM, 503 14.4
BOOTSTRAPPING IN REGRESSION, 508 14.4.1 BOOTSTRAP SAMPLING IN
REGRESSION, 509 CONTENTS XI 14.4.2 BOOTSTRAP CONFIDENCE INTERVALS, 510
14.5 CLASSIFICATION AND REGRESSION TREES (CART), 516 14.6 NEURAL
NETWORKS, 518 14.7 DESIGNED EXPERIMENTS FOR REGRESSION, 521 PROBLEMS,
524 15. VALIDATION OF REGRESSION MODELS 529 15.1 INTRODUCTION, 529 15.2
VALIDATION TECHNIQUES, 530 15.2.1 ANALYSIS OF MODEL COEFFICIENTS AND
PREDICTED VALUES, 530 15.2.2 COLLECTING FRESH DATA*CONFIRMATION RUNS,
532 15.2.3 DATA SPLITTING, 534 15.3 DATA FROM PLANNED EXPERIMENTS, 545
PROBLEMS, 545 APPENDIX A. STATISTICAL TABLES 549 APPENDIX B. DATA SETS
FOR EXERCISES 567 APPENDIX C. SUPPLEMENTAL TECHNICAL MATERIAL 582 C.I
BACKGROUND ON BASIC TEST STATISTICS, 582 C.2 BACKGROUND FROM THE THEORY
OF LINEAR MODELS, 585 C.3 IMPORTANT RESULTS ON SS R AND SS RES , 588 C.4
THE GAUSS-MARKOV THEOREM, VAR(S) = A 2 L, 594 C.5 COMPUTATIONAL ASPECTS
OF MULTIPLE REGRESSION, 595 C.6 A RESULT ON THE INVERSE OF A MATRIX, 597
C.7 DEVELOPMENT OF THE PRESS STATISTIC, 598 C.8 DEVELOPMENT OF S^, 600
C.9 AN OUTLIER TEST BASED ON /^-STUDENT, 601 CIO THE GAUSS-MARKOV
THEOREM, VAR(E) = V, 604 C.LL THE BIAS IN MS RES WHEN THE MODEL IS
UNDERSPECIFIED, 606 C.12 COMPUTATION OF INFLUENCE DIAGNOSTICS, 608 C.13
GENERALIZED LINEAR MODELS, 610 REFERENCES 621 INDEX 637
|
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| author | Montgomery, Douglas C. 1943- Peck, Elizabeth A. Vining, G. Geoffrey |
| author_GND | (DE-588)12861448X |
| author_facet | Montgomery, Douglas C. 1943- Peck, Elizabeth A. Vining, G. Geoffrey |
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| genre | (DE-588)4151278-9 Einführung gnd-content Lehrbuch - Lineare Regression |
| genre_facet | Einführung Lehrbuch - Lineare Regression |
| id | DE-604.BV014195355 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:21Z |
| institution | BVB |
| isbn | 0471315656 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009730278 |
| oclc_num | 248493159 |
| open_access_boolean | |
| owner | DE-703 DE-521 DE-634 |
| owner_facet | DE-703 DE-521 DE-634 |
| physical | XVI, 641 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Montgomery, Douglas C. 1943- Verfasser (DE-588)12861448X aut Introduction to linear regression analysis Douglas C. Montgomery ; Elizabeth A. Peck ; G. Geoffrey Vining 3. ed. New York [u.a.] Wiley 2001 XVI, 641 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Erg. bildet: Montgomery, Douglas C.: Student solutions manual to accompany Introduction to linear regression analysis Regression analysis Lineare Regression (DE-588)4167709-2 gnd rswk-swf Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Lehrbuch - Lineare Regression Lineare Regression (DE-588)4167709-2 s DE-604 Regressionsanalyse (DE-588)4129903-6 s 1\p DE-604 Lineares Regressionsmodell (DE-588)4127971-2 s 2\p DE-604 Peck, Elizabeth A. Verfasser aut Vining, G. Geoffrey Verfasser aut http://www.loc.gov/catdir/description/wiley034/00051312.html Publisher description http://www.loc.gov/catdir/toc/onix05/00051312.html Table of Contents HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009730278&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Montgomery, Douglas C. 1943- Peck, Elizabeth A. Vining, G. Geoffrey Introduction to linear regression analysis Regression analysis Lineare Regression (DE-588)4167709-2 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4167709-2 (DE-588)4127971-2 (DE-588)4129903-6 (DE-588)4151278-9 |
| title | Introduction to linear regression analysis |
| title_auth | Introduction to linear regression analysis |
| title_exact_search | Introduction to linear regression analysis |
| title_full | Introduction to linear regression analysis Douglas C. Montgomery ; Elizabeth A. Peck ; G. Geoffrey Vining |
| title_fullStr | Introduction to linear regression analysis Douglas C. Montgomery ; Elizabeth A. Peck ; G. Geoffrey Vining |
| title_full_unstemmed | Introduction to linear regression analysis Douglas C. Montgomery ; Elizabeth A. Peck ; G. Geoffrey Vining |
| title_short | Introduction to linear regression analysis |
| title_sort | introduction to linear regression analysis |
| topic | Regression analysis Lineare Regression (DE-588)4167709-2 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Regression analysis Lineare Regression Lineares Regressionsmodell Regressionsanalyse Einführung Lehrbuch - Lineare Regression |
| url | http://www.loc.gov/catdir/description/wiley034/00051312.html http://www.loc.gov/catdir/toc/onix05/00051312.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009730278&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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