Regression graphics: ideas for studying regressions through graphics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York u.a.
Wiley
1998
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| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of Contents Inhaltsverzeichnis |
| Beschreibung: | XVIII, 349 S. graph. Darst. |
| ISBN: | 0471193658 |
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| adam_text | IMAGE 1
REGRESSION GRAPHICS
IDEAS FOR STUDYING REGRESSIONS THROUGH GRAPHICS
R. DENNIS COOK THE UNIVERSITY OF MINNESOTA ST. PAUL, MINNESOTA
A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK *
CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO
IMAGE 2
CONTENTS
PREFACE 1. INTRODUCTION
1.1. C C & I, 1
1.1.1 CONSTRUCTION, 1 1.1.2 CHARACTERIZATION, 2 1.1.3 INFERENCE, 3 1.2.
ILLUSTRATIONS, 4 1.2.1 RESIDUAIS VERSUS FITTED VALUES, 4 1.2.2 RESIDUAIS
VERSUS THE PREDICTORS, 6 1.2.3 RESIDUAIS VERSUS THE RESPONSE, 7 1.3. ON
THINGS TO COME, 9 1.4. NOTATIONAL CONVENTIONS, 10 PROBLEMS, 13
2. INTRODUCTION TO 2D SCATTERPLOTS
2.1. RESPONSE PLOTS IN SIMPLE REGRESSION, 14 2.2. NEW ZEALAND HORSE
MUSSELS, 15 2.3. TRANSFORMING V VIA INVERSE RESPONSE PLOTS, 20 2.3.1
RESPONSE TRANSFORMATIONS, 21
2.3.2 RESPONSE TRANSFORMATIONS: MUSSEI DATA, 24 2.4. DANISH TWINS, 25
2.5. SCATTERPLOT MATRICES, 29
2.5.1 CONSTRUCTION, 29 2.5.2 EXAMPLE, 31
IMAGE 3
CONTENTS
2.6. REGRESSION GRAPHICS IN THE 1920S, 32
2.6.1 EZEKIEL S SUCCESSIVE APPROXIMATIONS, 32 2.6.2 BEAN S GRAPHIC
METHOD, 34 2.7. DISCUSSION, 37 PROBLEMS, 38
CONSTRUCTING 3D SCATTERPLOTS 40
3.1. GETTING AN IMPRESSION OF 3D, 40 3.2. DEPTH CUING, 42 3.3. SCALING,
43
3.4. ORTHOGONALIZATION, 44 PROBLEMS, 46
INTERPRETING 3D SCATTERPLOTS 47
4.1. HAYSTACKS, 47 4.2. STRUCTURAL DIMENSIONALITY, 49 4.2.1 ONE
PREDICTOR, 49 4.2.2 TWO PREDICTORS, 50
4.2.3 MANY PREDICTORS, 51 4.3. ONE-DIMENSIONAL STRUCTURE, 51 4.4.
TWO-DIMENSIONAL STRUCTURE, 55 4.4.1 REMOVING LINEAR TRENDS, 55
4.4.2 IDENTIFYING SEMIPARAMETRIC REGRESSION FUNCTIONS, 56 4.5. ASSESSING
STRUCTURAL DIMENSIONALITY, 58 4.5.1 A VISUAL METAPHOR FOR STRUCTURAL
DIMENSION, 59
4.5.2 A FIRST METHOD FOR DECIDING D = 1 OR 2, 59 4.5.3 NATURAL RUBBER,
61 4.6. ASSESSMENT METHODS, 63 4.6.1 USING INDEPENDENCE, 64
4.6.2 USING UNCORRELATED 2D VIEWS, 65 4.6.3 UNCORRELATED 2D VIEWS:
HAYSTACK DATA, 67 4.6.4 INTRASLICE RESIDUALS, 69 4.6.5 INTRASLICE
ORTHOGONALIZATION, 71
4.6.6 MUSSEIS AGAIN, 72 4.6.7 DISCUSSION, 73 PROBLEMS, 74
IMAGE 4
CONTENTS IX
5. BINARY RESPONSE VARIABLES 78
5.1. ONE PREDICTOR, 78 5.2. TWO PREDICTORS, 79 5.2.1 CHECKING OD
STRUCTURE, 82 5.2.2 CHECKING 1D STRUCTURE, 82
5.2.3 COMPARISON WITH PREVIOUS CHECKING METHODS, 84 5.2.4 EXPLOITING THE
BINARY RESPONSE, 85 5.3. ILLUSTRATIONS, 86
5.3.1 AUSTRALIAN INSTITUTE OF SPORT, 86 5.3.2 KYPHOSIS DATA, 89 5.4.
THREE PREDICTORS, 91 5.4.1 CHECKING 1D STRUCTURE, 91
5.4.2 KYPHOSIS DATA AGAIN, 93 5.5. VISUALIZING A LOGISTIC MODEL, 94
5.5.1 CONDITIONALLY NORMAL PREDICTORS, 95
5.5.2 OTHER PREDICTOR DISTRIBUTIONS, 98 PROBLEMS, 99
6. DIMENSION-REDUCTION SUBSPACES 101
6.1. OVERVIEW, 101 6.2. DIMENSION-REDUCTION SUBSPACES, 103 6.3. CENTRAL
SUBSPACES, 105 6.4. GUARANTEEING S , X BY CONSTRAINING ..., 108
6.4.1 ... THE DISTRIBUTION OF X, 108 6.4.2 ... THE DISTRIBUTION OF Y
X, 111 6.5. IMPORTANCE OF CENTRAL SUBSPACES, 112 6.6. /I-LEVEL RESPONSE
PLOTS, 114 PROBLEMS, 117
7. GRAPHICAL REGRESSION 120
7.1. INTRODUCTION TO GRAPHICAL REGRESSION, 120 7.2. CAPTURINGS^, 124
7.2.1 EXAMPLE: LINEAR REGRESSION, 125 7.2.2 EXAMPLE: S Y[XI = S(.VI),
BUT S Y]X2 S(RJ 2 ), 126
7.3. FORCING S Y]XI E S^), 127
7.3.1 LOCATION REGRESSIONS FOR THE PREDICTORS, 128 7.3.2 ELLIPTICALLY
CONTOURED DISTRIBUTIONS, 129 7.3.3 ELLIPTICALLY CONTOURED PREDICTORS,
131
IMAGE 5
X
CONTENTS
7.4. IMPROVING RESOLUTION, 134
7.5. FORCING S Y]XI = S^), 131
7.5.1 EXAMPLE: X { INDEPENDENT OF X 2 , BUT SYTO*STOI). 137
7.5.2 CONDITIONSFORS^ =5(7?,), 137 7.5.3 MARGINAL CONSISTENCY
ASSUMPTION, 139 7.6. VISUAL FITTING WITH /I-LEVEL RESPONSE PLOTS, 140
PROBLEMS, 142
8. GETTING NUMERICAL HELP 143
8.1. FITTING WITH LINEAR KERNEIS, 143 8.1.1 ISOMERIZATION DATA, 145
8.1.2 USING THE LI-DUAN PROPOSITION, 146 8.2. QUADRATIC KERNEIS, 147
8.3. THE PREDICTOR DISTRIBUTION, 150 8.4. REWEIGHTING FOR ELLIPTICAL
CONTOURS, 153
8.4.1 VORONOI WEIGHTS, 154 8.4.2 TARGET DISTRIBUTION, 155 8.4.3
MODIFYING THE PREDICTORS, 156 PROBLEMS, 158
9. GRAPHICAL REGRESSION STUDIES 159
9.1. NAPHTHALENE DATA, 159 9.1.1 NAPHTHOQUINONE, Y N , 161 9.1.2
PHTHALIC ANHYDRIDE, Y P , 170 9.2. WHEAT PROTEIN, 175 9.3. REACTION
YIELD, 179 9.4. DISCUSSION, 184
PROBLEMS, 184
10. INVERSE REGRESSION GRAPHICS 187
10.1. INVERSE REGRESSION FUNCTION, 187 10.1.1 MEAN CHECKING CONDITION,
191 10.1.2 MEAN CHECKING CONDITION: WHEAT PROTEIN, 193 10.1.3 MEAN
CHECKING CONDITION: MUSSEI DATA, 194 10.2. INVERSE VARIANCE FUNCTION,
196
10.2.1 VARIANCE CHECKING CONDITION, 199 10.2.2 VARIANCE CHECKING
CONDITION: ETHANOL DATA, 200 PROBLEMS, 201
IMAGE 6
CONTENTS XI
11. SLICED INVERSE REGRESSION 203
11.1. INVERSE REGRESSION SUBSPACE, 203 11.2. SIR, 204 11.3. ASYMPTOTIC
DISTRIBUTION OF A D , 206 11.3.1 OVERVIEW, 206
11.3.2 THE GENERAL CASE, 208 11.3.3 DISTRIBUTION OF A D WITH
CONSTRAINTS, 210 11.4. SIR: MUSSEI DATA, 213 11.5. MINNEAPOLIS SCHOOLS,
216 11.6. DISCUSSION, 220 PROBLEMS, 222
12. PRINCIPAL HESSIAN DIRECTIONS 224
12.1. INCORPORATING RESIDUALS, 225 12.2. CONNECTING S E Z AND S EZZ
WHEN .... 227
12.2.1 ...E(Z P R Z) = P P Z, 227 12.2.2 ... E(Z | P T Z) = P P Z AND
VAR(Z | P T Z) = Q P , 230 12.2.3 ... Z IS NORMALLY DISTRIBUTED, 231
12.3. ESTIMATION AND TESTING, 231 12.3.1 ASYMPTOTIC DISTRIBUTION OF A K
, 232 12.3.2 AN ALGORITHM FOR INFERENCE ON K, 235 12.3.3 ASYMPTOTIC
DISTRIBUTION OF A K WITH
CONSTRAINTS, 236 12.3.4 TESTING E INDEPENDENT OF Z, 238 12.4. PHD:
REACTION YIELD, 238 12.4.1 OLS AND SIR, 239
12.4.2 PHD TEST RESULTS, 240 12.4.3 SUBTRACTING SS, 241 12.4.4 USING
STRONGER ASSUMPTIONS, 243 12.5. PHD: MUSSEI DATA, 243 12.5.1 PHD TEST
RESULTS, 244 12.5.2 SIMULATING THE RESPONSE, 246 12.5.3 USING VORONOI
WEIGHTS, 246 12.6. PHD: HAYSTACKS, 248 12.7. DISCUSSION, 249 12.7.1 PHD
WITH THE RESPONSE, 249 12.7.2 ADDITIONAL DEVELOPMENTS, 250 PROBLEMS, 251
IMAGE 7
XII
CONTENTS
13. STUDYING PREDICTOR EFFECTS 254
13.1. INTRODUCTION TO NET-EFFECT PLOTS, 254 13.1.1 NATURAL RUBBER:
NET-EFFECT PLOTS, 255 13.1.2 JOINT NORMALITY, 256 13.1.3 SLICING, 257
13.1.4 REDUCING BRUSHING DIMENSIONS, 259 13.2. DISTRIBUTIONAL INDICES,
259
13.2.1 EXAMPLE, 260 13.2.2 LOCATION DEPENDENCE, 262 13.2.3 POST-MODEL
NET-EFFECT PLOTS, 264 13.2.4 BIVARIATE SIR, 265 13.3. GLOBAL NET-EFFECT
PLOTS, 266
13.3.1 TAR, 268 13.3.2 MINNEAPOLIS SCHOOLS AGAIN, 269 PROBLEMS, 270
14. PREDICTOR TRANSFORMATIONS 272
14.1. CERES PLOTS, 273 14.1.1 MOTIVATION, 273 14.1.2 ESTIMATING A V 274
14.1.3 EXAMPLE, 276 14.2. CERES PLOTS WHEN E(^ | X 2 ) IS ..., 279
14.2.1 ... CONSTANT, 279 14.2.2 ... LINEAR IN X 2 , 280 14.2.3 ...
QUADRATIC IN X 2 , 281 14.3. CERES PLOTS IN PRACTICE, 283
14.3.1 HIGHLY DEPENDENT PREDICTORS, 284 14.3.2 USING MANY CERES PLOTS,
285 14.3.3 TRANSFORMING MORE THAN ONE PREDICTOR, 289 14.4. BIG MAC DATA,
290 14.5. ADDED-VARIABLE PLOTS, 294 14.6. ENVIRONMENTAL CONTAMINATION,
296 14.6.1 ASSESSING RELATIVE IMPORTANCE, 297 14.6.2 DATA ANALYSIS, 298
PROBLEMS, 302
IMAGE 8
CONTENTS
XIII
15. GRAPHICS FOR MODEL ASSESSMENT 303
15.1. RESIDUALPLOTS, 304 15.1.1 RATIONALE, 304 15.1.2 ISOMERIZATION
DATA, 305 15.1.3 USING RESIDUALS IN GRAPHICAL REGRESSION, 306 15.1.4
PHD, 309 15.1.5 RESIDUAL PLOTS: KYPHOSIS DATA, 309 15.1.6 INTERPRETING
RESIDUAL PLOTS, 312 15.2. ASSESSING MODEL ADEQUACY, 313
15.2.1 MARGINAL REGRESSION FUNCTIONS ... , 314 15.2.2 MARGINAL VARIANCE
FUNCTIONS ... ,316 15.2.3 MARGINAL MODEL PLOTS, 317 15.2.4 ISOMERIZATION
DATA AGAIN, 319 15.2.5 REACTION YIELD DATA, 322 15.2.6 TOMATO TOPS, 322
15.2.7 MARGINAL MODEL PLOTS: KYPHOSIS DATA, 325 PROBLEMS, 327
BIBLIOGRAPHY 329
AUTHOR INDEX 339
SUBJECT INDEX 343
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:37:40Z |
| institution | BVB |
| isbn | 0471193658 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008866143 |
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| owner_facet | DE-384 DE-19 DE-BY-UBM DE-521 DE-83 DE-91G DE-BY-TUM |
| physical | XVIII, 349 S. graph. Darst. |
| publishDate | 1998 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and statistics |
| spelling | Cook, Robert D. Verfasser aut Regression graphics ideas for studying regressions through graphics R. Dennis Cook New York u.a. Wiley 1998 XVIII, 349 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Regression analysis -- Graphic methods Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Grafische Darstellung (DE-588)4129552-3 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Grafische Darstellung (DE-588)4129552-3 s DE-604 http://www.loc.gov/catdir/description/wiley032/98003628.html Publisher description http://www.loc.gov/catdir/toc/onix02/98003628.html Table of Contents GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008866143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cook, Robert D. Regression graphics ideas for studying regressions through graphics Regression analysis -- Graphic methods Regressionsanalyse (DE-588)4129903-6 gnd Grafische Darstellung (DE-588)4129552-3 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4129552-3 |
| title | Regression graphics ideas for studying regressions through graphics |
| title_auth | Regression graphics ideas for studying regressions through graphics |
| title_exact_search | Regression graphics ideas for studying regressions through graphics |
| title_full | Regression graphics ideas for studying regressions through graphics R. Dennis Cook |
| title_fullStr | Regression graphics ideas for studying regressions through graphics R. Dennis Cook |
| title_full_unstemmed | Regression graphics ideas for studying regressions through graphics R. Dennis Cook |
| title_short | Regression graphics |
| title_sort | regression graphics ideas for studying regressions through graphics |
| title_sub | ideas for studying regressions through graphics |
| topic | Regression analysis -- Graphic methods Regressionsanalyse (DE-588)4129903-6 gnd Grafische Darstellung (DE-588)4129552-3 gnd |
| topic_facet | Regression analysis -- Graphic methods Regressionsanalyse Grafische Darstellung |
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