Introduction to linear regression analysis:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Wiley
1992
|
| Edition: | 2. ed. |
| Series: | Wiley series in probability and mathematical statistics
A Wiley interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 527 S. graph. Darst. |
| ISBN: | 0471533874 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to linear regression analysis |c Douglas C. Montgomery ; Elizabeth A. Peck |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Wiley |c 1992 | |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 1.1 REGRESSION AND MODEL BUILDING, 1 1.2 USES OF
REGRESSION, 5 1.3 ROLE OF THE COMPUTER, 6
2. SIMPLE LINEAR REGRESSION AND CORRELATION
2.1 SIMPLE LINEAR REGRESSION MODEL, 7 2.2 LEAST SQUARES ESTIMATION OF
THE PARAMETERS, 8 2.2.1 ESTIMATION OF P 0 AND /3,, 8 2.2.2 PROPERTIES OF
THE LEAST SQUARES ESTIMATORS AND THE
FITTED REGRESSION MODEL, 13 2.2.3 ESTIMATION OF A 2 , 15 2.2.4 AN
ALTERNATE FORM OF THE MODEL, 17 2.3 HYPOTHESIS TESTING ON THE SLOPE AND
INTERCEPT, 18 2.4 INTERVAL ESTIMATION IN SIMPLE LINEAR REGRESSION, 24
2.4.1 CONFIDENCE INTERVALS ON /3 0 , J3,, AND R 2 , 24 2.4.2 INTERVAL
ESTIMATION OF THE MEAN RESPONSE, 26 2.5 PREDICTION OF NEW OBSERVATIONS,
30 2.6 SIMULTANEOUS INFERENCE IN SIMPLE LINEAR REGRESSION, 32
2.6.1 SIMULTANEOUS INFERENCE ON MODEL PARAMETERS, 32 2.6.2 SIMULTANEOUS
ESTIMATION OF MEAN RESPONSE, 38 2.6.3 PREDICTION OF M NEW OBSERVATIONS,
39 2.7 COEFFICIENT OF DETERMINATION, 40 2.8 HAZARDS IN THE USE OF
REGRESSION, 42 2.9 REGRESSION THROUGH THE ORIGIN, 45 2.10 ESTIMATION BY
MAXIMUM LIKELIHOOD, 51 2.11 CORRELATION, 52 2.12 SAMPLE COMPUTER OUTPUT,
57 PROBLEMS, 60
IMAGE 2
3. MEASURES OF MODEL ADEQUACY 67
3.1 INTRODUCTION, 67 3.2 RESIDUAL ANALYSIS, 68 3.2.1 DEFINITION OF
RESIDUALS, 68 3.2.2 NORMAL PROBABILITY PLOT, 69
3.2.3 PLOT OF RESIDUALS AGAINST Y,, 74 3.2.4 PLOT OF RESIDUALS AGAINST
*,-, 75 3.2.5 OTHER RESIDUAL PLOTS, 77
3.2.6 STATISTICAL TESTS ON RESIDUALS, 79 3.3 DETECTION AND TREATMENT OF
OUTLIERS, 80 3.4 A TEST FOR LACK OF FIT, 85 3.5 TRANSFORMATIONS TO A
STRAIGHT LINE, 89 3.6 VARIANCE-STABILIZING TRANSFORMATIONS, 98 3.7
ANALYTICAL METHODS FOR SELECTING A TRANSFORMATION, 103
3.7.1 TRANSFORMATIONS ON Y, 103 3.7.2 TRANSFORMATIONS ON X, 105 3.8
WEIGHTED LEAST SQUARES, 108 PROBLEMS, 113
4. MULTIPLE LINEAR REGRESSION 118
4.1 MULTIPLE REGRESSION MODELS, 118 4.2 ESTIMATION OF THE MODEL
PARAMETERS, 120 4.2.1 LEAST SQUARES ESTIMATION OF THE REGRESSION
COEFFICIENTS, 120
4.2.2 A GEOMETRICAL INTERPRETATION OF LEAST SQUARES, 127 4.2.3
PROPERTIES OF THE LEAST SQUARES ESTIMATORS, 128 4.2.4 ESTIMATION OF A- 2
, 129
4.2.5 INADEQUACY OF SCATTER DIAGRAMS IN MULTIPLE REGRESSION, 130 4.3
CONFIDENCE INTERVALS IN MULTIPLE REGRESSION, 132 4.3.1 CONFIDENCE
INTERVALS ON THE REGRESSION
COEFFICIENTS, 132 4.3.2 CONFIDENCE INTERVAL ESTIMATION OF THE MEAN
RESPONSE, 133 4.4 HYPOTHESIS TESTING IN MULTIPLE LINEAR REGRESSION, 135
4.4.1 TEST FOR SIGNIFICANCE OF REGRESSION, 135 4.4.2 TESTS ON INDIVIDUAL
REGRESSION COEFFICIENTS, 138 4.4.3 SPECIAL CASE OF ORTHOGONAL COLUMNS IN
X, 143 4.4.4 TESTING THE GENERAL LINEAR HYPOTHESIS
T/3 = 0, 145
IMAGE 3
4.5 PREDICTION OF NEW OBSERVATIONS, 148
4.6 HIDDEN EXTRAPOLATION, 148 4.7 SIMULTANEOUS INFERENCE IN MULTIPLE
REGRESSION, 152 4.7.1 SIMULTANEOUS CONFIDENCE REGION ON COEFFICIENTS,
152
4.7.2 BONFERRONI, SCHEFFE, AND MAXIMUM MODULUS T INTERVALS, 152 4.7.3
SIMULTANEOUS ESTIMATION OF MEAN RESPONSE, 153 4.7.4 PREDICTION OF M NEW
OBSERVATIONS, 154 4.8 STANDARDIZED REGRESSION COEFFICIENTS, 155 4.9
REGRESSION DIAGNOSTICS AND MEASURES OF MODEL
ADEQUACY, 159 4.9.1 COEFFICIENT OF MULTIPLE DETERMINATION, 159 4.9.2
RESIDUAL PLOTS, 161 4.9.3 METHODS FOR SCALING RESIDUALS, 169 4.9.4
ESTIMATION OF PURE ERROR FROM
NEAR-NEIGHBORS, 177 4.9.5 INFLUENCE DIAGNOSTICS, 179 4.9.6
MULTICOLLINEARITY, 189 4.10 SAMPLE COMPUTER OUTPUT, 192
PROBLEMS, 195
5. POLYNOMIAL REGRESSION MODELS 202
5.1 INTRODUCTION, 202 5.2 POLYNOMIAL MODELS IN ONE VARIABLE, 202 5.2.1
BASIC PRINCIPLES, 202 5.2.2 PIECEWISE POLYNOMIAL FITTING (SPLINES), 210
5.3 POLYNOMIAL MODELS IN TWO OR MORE VARIABLES, 218 5.4 ORTHOGONAL
POLYNOMIALS, 226 PROBLEMS, 231
6. INDICATOR VARIABLES 237
6.1 THE GENERAL CONCEPT OF INDICATOR VARIABLES, 237 6.2 COMMENTS ON THE
USE OF INDICATOR VARIABLES, 252 6.2.1 INDICATOR VARIABLES VERSUS
REGRESSION ON ALLOCATED CODES, 252
6.2.2 INDICATOR VARIABLES AS A SUBSTITUTE FOR A QUANTITATIVE REGRESSOR,
253 6.2.3 MODELS WITH ONLY INDICATOR VARIABLES, 253
IMAGE 4
6.3 REGRESSION MODELS WITH AN INDICATOR RESPONSE VARIABLE,
254 6.3.1 A LINEAR MODEL, 255 6.3.2 A NONLINEAR MODEL, 258 PROBLEMS, 262
7. VARIABLE SELECTION AND MODEL BUILDING 265
7.1 INTRODUCTION, 265 7.1.1 MODEL-BUILDING PROBLEM, 265 7.1.2
CONSEQUENCES OF MODEL MISSPECIFICATION, 266 7.1.3 CRITERIA FOR
EVALUATING SUBSET REGRESSION
MODELS, 270
7.2 COMPUTATIONAL TECHNIQUES FOR VARIABLE SELECTION, 275 7.2.1 ALL
POSSIBLE REGRESSIONS, 276 7.2.2 DIRECTED SEARCH ON T, 286 7.2.3 STEPWISE
REGRESSION METHODS, 290 7.2.4 OTHER PROCEDURES, 298
7.3 SOME FINAL CONSIDERATIONS, 300 PROBLEMS, 302
8. MULTICOLLINEARITY 305
8.1 INTRODUCTION, 305 8.2 SOURCES OF MULTICOLLINEARITY, 305 8.3 EFFECTS
OF MULTICOLLINEARITY, 308 8.4 MULTICOLLINEARITY DIAGNOSTICS, 314
8.4.1 EXAMINATION OF THE CORRELATION MATRIX, 314 8.4.2 VARIANCE
INFLATION FACTORS, 317 8.4.3 EIGENSYSTEM ANALYSIS OF X X, 318 8.4.4
OTHER DIAGNOSTICS, 323 8.5 METHODS FOR DEALING WITH MULTICOLLINEARITY,
325
8.5.1 COLLECTING ADDITIONAL DATA, 325 8.5.2 MODEL RESPECIFICATION, 326
8.5.3 RIDGE REGRESSION, 329 8.5.4 GENERALIZED RIDGE REGRESSION, 344
8.5.5 PRINCIPAL COMPONENTS REGRESSION, 353
8.5.6 LATENT ROOT REGRESSION ANALYSIS, 357 8.5.7 COMPARISON AND
EVALUATION OF BIASED ESTIMATORS, 358
PROBLEMS, 361
IMAGE 5
9. TOPICS IN THE USE OF REGRESSION ANALYSIS 365
9.1 AUTOCORRELATION, 366 9.1.1 SOURCE AND EFFECTS OF AUTOCORRELATION,
366 9.1.2 DETECTING THE PRESENCE OF AUTOCORRELATION, 367 9.1.3 PARAMETER
ESTIMATION METHODS, 372
9.2 GENERALIZED AND WEIGHTED LEAST SQUARES, 378 9.3 ROBUST REGRESSION,
382 9.3.1 THE NEED FOR ROBUST ESTIMATION, 382 9.3.2 AF-ESTIMATORS, 384
9.3.3 R- AND L-ESTIMATION, 397 9.3.4 ROBUST RIDGE REGRESSION, 398 9.4
WHY DO REGRESSION COEFFICIENTS HAVE THE WRONG SIGN?, 399 9.5 EFFECT OF
MEASUREMENT ERRORS IN THE X S, 402 9.6 INVERSE ESTIMATION (CALIBRATION
OR DISCRIMINATION), 404 9.7 DESIGNED EXPERIMENTS FOR REGRESSION, 409 9.8
RELATIONSHIP BETWEEN REGRESSION AND ANALYSIS
OF VARIANCE, 411 9.9 GENERALIZED LINEAR MODELS, 418 9.10 AN INTRODUCTION
TO NONLINEAR REGRESSION, 421 9.10.1 NONLINEAR REGRESSION MODEL, 421
9.10.2 NONLINEAR LEAST SQUARES, 422 9.10.3 TRANSFORMING TO A LINEAR
MODEL, 423 9.10.4 PARAMETER ESTIMATION IN A NONLINEAR SYSTEM, 426 9.10.5
STARTING VALUES, 431 9.10.6 EXAMPLES OF NONLINEAR REGRESSION MODELS, 432
PROBLEMS, 433
10. VALIDATION OF REGRESSION MODELS 443
10.1 INTRODUCTION, 443 10.2 VALIDATION TECHNIQUES, 444 10.2.1 ANALYSIS
OF MODEL COEFFICIENTS AND PREDICTED VALUES, 445
10.2.2 COLLECTING FRESH DATA, 446 10.2.3 DATA SPLITTING, 448 10.3 DATA
FROM PLANNED EXPERIMENTS, 458 PROBLEMS, 459
APPENDIX A STATISTICAL TABLES 463
APPENDIX B DATA SETS FOR EXERCISES 486
IMAGE 6
APPENDIX C SUPPLEMENTAL TECHNICAL MATERIAL
C.I COMPUTATIONAL ASPECTS OF MULTIPLE
498
REFERENCES
INDEX
C.2 C.3 C.4 C.5
REGRESSION, 498 A RESULT ON THE INVERSE OF A MATRIX, 500 DEVELOPMENT OF
THE PRESS STATISTIC, 501 DEVELOPMENT OF SF IY , 503
COMPUTATION OF INFLUENCE DIAGNOSTICS, 504
507
523
|
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| author | Montgomery, Douglas C. 1943- Peck, Elizabeth A. 1953- |
| author_GND | (DE-588)12861448X (DE-588)135772702 |
| author_facet | Montgomery, Douglas C. 1943- Peck, Elizabeth A. 1953- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5/36 20 519.5/36 |
| dewey-sort | 3519.5 236 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| indexdate | 2024-07-09T17:15:42Z |
| institution | BVB |
| isbn | 0471533874 |
| language | English |
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| series2 | Wiley series in probability and mathematical statistics A Wiley interscience publication |
| spelling | Montgomery, Douglas C. 1943- Verfasser (DE-588)12861448X aut Introduction to linear regression analysis Douglas C. Montgomery ; Elizabeth A. Peck 2. ed. New York u.a. Wiley 1992 XIV, 527 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics A Wiley interscience publication Analyse de régression Analyse de régression ram Lineaire regressie gtt Regressieanalyse gtt Regression analysis Lineare Regression (DE-588)4167709-2 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Regressionsanalyse (DE-588)4129903-6 s DE-604 Lineares Regressionsmodell (DE-588)4127971-2 s Lineare Regression (DE-588)4167709-2 s Peck, Elizabeth A. 1953- Verfasser (DE-588)135772702 aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005390783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Montgomery, Douglas C. 1943- Peck, Elizabeth A. 1953- Introduction to linear regression analysis Analyse de régression Analyse de régression ram Lineaire regressie gtt Regressieanalyse gtt Regression analysis Lineare Regression (DE-588)4167709-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| subject_GND | (DE-588)4167709-2 (DE-588)4129903-6 (DE-588)4127971-2 (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 |
| title_fullStr | Introduction to linear regression analysis Douglas C. Montgomery ; Elizabeth A. Peck |
| title_full_unstemmed | Introduction to linear regression analysis Douglas C. Montgomery ; Elizabeth A. Peck |
| title_short | Introduction to linear regression analysis |
| title_sort | introduction to linear regression analysis |
| topic | Analyse de régression Analyse de régression ram Lineaire regressie gtt Regressieanalyse gtt Regression analysis Lineare Regression (DE-588)4167709-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| topic_facet | Analyse de régression Lineaire regressie Regressieanalyse Regression analysis Lineare Regression Regressionsanalyse Lineares Regressionsmodell Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005390783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT montgomerydouglasc introductiontolinearregressionanalysis AT peckelizabetha introductiontolinearregressionanalysis |