Applied regression analysis: a research tool
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon
Springer
1998
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer texts in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 635 - 646 |
| Beschreibung: | XVIII, 657 S. graph. Darst. |
| ISBN: | 0387984542 |
Internformat
MARC
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| 100 | 1 | |a Rawlings, John O. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied regression analysis |b a research tool |c John O. Rawlings ; Sastry G. Pantula ; David A. Dickey |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon |b Springer |c 1998 | |
| 300 | |a XVIII, 657 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer texts in statistics | |
| 500 | |a Literaturverz. S. 635 - 646 | ||
| 650 | 4 | |a Analyse de régression | |
| 650 | 7 | |a Regressieanalyse |2 gtt | |
| 650 | 4 | |a Regression analysis | |
| 650 | 0 | 7 | |a Regressionsanalyse |0 (DE-588)4129903-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Pantula, Sastry G. |e Verfasser |4 aut | |
| 700 | 1 | |a Dickey, David A. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804126655816400896 |
|---|---|
| adam_text | Contents
PREFACE vii
1 REVIEW OF SIMPLE REGRESSION 1
1.1 The Linear Model and Assumptions 2
1.2 Least Squares Estimation 3
1.3 Predicted Values and Residuals 6
1.4 Analysis of Variation in the Dependent Variable 7
1.5 Precision of Estimates 11
1.6 Tests of Significance and Confidence Intervals 16
1.7 Regression Through the Origin 21
1.8 Models with Several Independent Variables 27
1.9 Violation of Assumptions 28
1.10 Summary 29
1.11 Exercises 30
2 INTRODUCTION TO MATRICES 37
2.1 Basic Definitions 37
2.2 Special Types of Matrices 39
2.3 Matrix Operations 40
2.4 Geometric Interpretations of Vectors 46
2.5 Linear Equations and Solutions 50
2.6 Orthogonal Transformations and Projections 54
2.7 Eigenvalues and Eigenvectors 57
2.8 Singular Value Decomposition 60
xiv Contents
2.9 Summary 68
2.10 Exercises 68
3 MULTIPLE REGRESSION IN MATRIX NOTATION 75
3.1 The Model 75
3.2 The Normal Equations and Their Solution 78
3.3 The Y and Residuals Vectors 80
3.4 Properties of Linear Functions of Random Vectors 82
3.5 Properties of Regression Estimates 87
3.6 Summary of Matrix Formulae 92
3.7 Exercises 93
4 ANALYSIS OF VARIANCE AND QUADRATIC FORMS 101
4.1 Introduction to Quadratic Forms 102
4.2 Analysis of Variance 107
4.3 Expectations of Quadratic Forms 113
4.4 Distribution of Quadratic Forms 115
4.5 General Form for Hypothesis Testing 119
4.5.1 The General Linear Hypothesis 119
4.5.2 Special Cases of the General Form 121
4.5.3 A Numerical Example 122
4.5.4 Computing Q from Differences in Sums of Squares . 126
4.5.5 The i? Notation to Label Sums of Squares 129
4.5.6 Example: Sequential and Partial Sums of Squares . . 133
4.6 Univariate and Joint Confidence Regions 135
4.6.1 Univariate Confidence Intervals 135
4.6.2 Simultaneous Confidence Statements 137
4.6.3 Joint Confidence Regions 139
4.7 Estimation of Pure Error 143
4.8 Exercises 149
5 CASE STUDY: FIVE INDEPENDENT VARIABLES 161
5.1 Spartina Biomass Production in the Cape Fear Estuary . . 161
5.2 Regression Analysis for the Full Model 162
5.2.1 The Correlation Matrix 164
5.2.2 Multiple Regression Results: Full Model 165
5.3 Simplifying the Model 167
5.4 Results of the Final Model 170
5.5 General Comments 177
5.6 Exercises 179
6 GEOMETRY OF LEAST SQUARES 183
6.1 Linear Model and Solution 184
6.2 Sums of Squares and Degrees of Freedom 189
6.3 Reparameterization 192
Contents xv
6.4 Sequential Regressions 196
6.5 The Collinearity Problem 197
6.6 Summary 201
6.7 Exercises 201
7 MODEL DEVELOPMENT: VARIABLE SELECTION 205
7.1 Uses of the Regression Equation 206
7.2 Effects of Variable Selection on Least Squares 208
7.3 All Possible Regressions 210
7.4 Stepwise Regression Methods 213
7.5 Criteria for Choice of Subset Size 220
7.5.1 Coefficient of Determination 220
7.5.2 Residual Mean Square 222
7.5.3 Adjusted Coefficient of Determination 222
7.5.4 Mallows Cp Statistic 223
7.5.5 Information Criteria: AIC and SBC 225
7.5.6 Significance Levels for Choice of Subset Size . . . 226
7.6 Model Validation 228
7.7 Exercises 231
8 POLYNOMIAL REGRESSION 235
8.1 Polynomials in One Variable 236
8.2 Trigonometric Regression Models 245
8.3 Response Curve Modeling 249
8.3.1 Considerations in Specifying the Functional Form . . 249
8.3.2 Polynomial Response Models 250
8.4 Exercises 262
9 CLASS VARIABLES IN REGRESSION 269
9.1 Description of Class Variables 270
9.2 The Model for One Way Structured Data 271
9.3 Reparameterizing to Remove Singularities 273
9.3.1 Reparameterizing with the Means Model 274
9.3.2 Reparameterization Motivated by ]JP n = 0 277
9.3.3 Reparameterization Motivated by rt = 0 279
9.3.4 Reparameterization: A Numerical Example 280
9.4 Generalized Inverse Approach 282
9.5 The Model for Two Way Classified Data 284
9.6 Class Variables to Test Homogeneity of Regressions 288
9.7 Analysis of Covariance 294
9.8 Numerical Examples 300
9.8.1 Analysis of Variance 301
9.8.2 Test of Homogeneity of Regression Coefficients . . . 306
9.8.3 Analysis of Covariance 307
9.9 Exercises 316
xvi Contents
10 PROBLEM AREAS IN LEAST SQUARES 325
10.1 Nonnormality 326
10.2 Heterogeneous Variances 328
10.3 Correlated Errors 329
10.4 Influential Data Points and Outliers 330
10.5 Model Inadequacies 332
10.6 The Collinearity Problem 333
10.7 Errors in the Independent Variables 334
10.8 Summary 339
10.9 Exercises 339
11 REGRESSION DIAGNOSTICS 341
11.1 Residuals Analysis 342
11.1.1 Plot of e Versus Y 346
11.1.2 Plots of e Versus Xt 350
11.1.3 Plots of e Versus Time 351
11.1.4 Plots of a Versus et i 354
11.1.5 Normal Probability Plots 356
11.1.6 Partial Regression Leverage Plots 359
11.2 Influence Statistics 361
11.2.1 Cook s D 362
11.2.2 DFFITS 363
11.2.3 DFBETAS 364
11.2.4 COVRATIO 364
11.2.5 Summary of Influence Measures 367
11.3 Collinearity Diagnostics 369
11.3.1 Condition Number and Condition Index 371
11.3.2 Variance Inflation Factor 372
11.3.3 Variance Decomposition Proportions 373
11.3.4 Summary of Collinearity Diagnostics 377
11.4 Regression Diagnostics on the Linthurst Data 377
11.4.1 Plots of Residuals 378
11.4.2 Influence Statistics 388
11.4.3 Collinearity Diagnostics 391
11.5 Exercises 392
12 TRANSFORMATION OF VARIABLES 397
12.1 Reasons for Making Transformations 397
12.2 Transformations to Simplify Relationships 399
12.3 Transformations to Stabilize Variances 407
12.4 Transformations to Improve Normality 409
12.5 Generalized Least Squares 412
12.5.1 Weighted Least Squares 414
12.5.2 Generalized Least Squares 417
12.6 Summary 426
Contents xvii
12.7 Exercises 427
13 COLLINEARITY 433
13.1 Understanding the Structure of the X Space 435
13.2 Biased Regression 443
13.2.1 Explanation 443
13.2.2 Principal Component Regression 446
13.3 General Comments on Collinearity 457
13.4 Summary 459
13.5 Exercises 459
14 CASE STUDY: COLLINEARITY PROBLEMS 463
14.1 The Problem 463
14.2 Multiple Regression: Ordinary Least Squares 467
14.3 Analysis of the Correlational Structure 471
14.4 Principal Component Regression 479
14.5 Summary 482
14.6 Exercises 483
15 MODELS NONLINEAR IN THE PARAMETERS 485
15.1 Examples of Nonlinear Models 486
15.2 Fitting Models Nonlinear in the Parameters 494
15.3 Inference in Nonlinear Models 498
15.4 Violation of Assumptions 507
15.4.1 Heteroscedastic Errors 507
15.4.2 Correlated Errors 509
15.5 Logistic Regression 509
15.6 Exercises 511
16 CASE STUDY: RESPONSE CURVE MODELING 515
16.1 The Ozone Sulfur Dioxide Response Surface (1981) 517
16.1.1 Polynomial Response Model 520
16.1.2 Nonlinear Weibull Response Model 524
16.2 Analysis of the Combined Soybean Data 530
16.3 Exercises 543
17 ANALYSIS OF UNBALANCED DATA 545
17.1 Sources of Imbalance 546
17.2 Effects of Imbalance 547
17.3 Analysis of Cell Means 549
17.4 Linear Models for Unbalanced Data 553
17.4.1 Estimable Functions with Balanced Data 554
17.4.2 Estimable Functions with Unbalanced Data 558
17.4.3 Least Squares Means 564
17.5 Exercises 568
xviii Contents
18 MIXED EFFECTS MODELS 573
18.1 Random Effects Models 574
18.2 Fixed and Random Effects 579
18.3 Random Coefficient Regression Models 584
18.4 General Mixed Linear Models 586
18.5 Exercises 589
19 CASE STUDY: ANALYSIS OF UNBALANCED DATA 593
19.1 The Analysis of Variance 596
19.2 Mean Square Expectations and Choice of Errors 607
19.3 Least Squares Means and Standard Errors 610
19.4 Mixed Model Analysis 615
19.5 Exercises 618
A APPENDIX TABLES 621
References 635
Author Index 647
Subject Index 650
|
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| author | Rawlings, John O. Pantula, Sastry G. Dickey, David A. |
| author_facet | Rawlings, John O. Pantula, Sastry G. Dickey, David A. |
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| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)38073341 (DE-599)BVBBV012058166 |
| dewey-full | 519.5/36 519.5/3621 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/36 519.5/36 21 |
| dewey-search | 519.5/36 519.5/36 21 |
| dewey-sort | 3519.5 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV012058166 |
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| indexdate | 2024-07-09T18:20:55Z |
| institution | BVB |
| isbn | 0387984542 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008161202 |
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| publishDate | 1998 |
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| spelling | Rawlings, John O. Verfasser aut Applied regression analysis a research tool John O. Rawlings ; Sastry G. Pantula ; David A. Dickey 2. ed. New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon Springer 1998 XVIII, 657 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Literaturverz. S. 635 - 646 Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s DE-604 Schätztheorie (DE-588)4121608-8 s 1\p DE-604 Pantula, Sastry G. Verfasser aut Dickey, David A. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161202&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 | Rawlings, John O. Pantula, Sastry G. Dickey, David A. Applied regression analysis a research tool Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4121608-8 |
| title | Applied regression analysis a research tool |
| title_auth | Applied regression analysis a research tool |
| title_exact_search | Applied regression analysis a research tool |
| title_full | Applied regression analysis a research tool John O. Rawlings ; Sastry G. Pantula ; David A. Dickey |
| title_fullStr | Applied regression analysis a research tool John O. Rawlings ; Sastry G. Pantula ; David A. Dickey |
| title_full_unstemmed | Applied regression analysis a research tool John O. Rawlings ; Sastry G. Pantula ; David A. Dickey |
| title_short | Applied regression analysis |
| title_sort | applied regression analysis a research tool |
| title_sub | a research tool |
| topic | Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Analyse de régression Regressieanalyse Regression analysis Regressionsanalyse Schätztheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161202&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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