Introduction to linear regression analysis:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Hoboken, NJ
Wiley-Blackwell
2012
|
| Ausgabe: | 5. ed. |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021211686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 645 S. graph. Darst. |
| ISBN: | 9780470542811 |
Internformat
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| 245 | 1 | 0 | |a Introduction to linear regression analysis |c Douglas C. Montgomery ; Elizabeth A. Peck ; G. Geoffrey Vining |
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Datensatz im Suchindex
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| adam_text | CONTENTS
PREFACE xiii
1. INTRODUCTION 1
1.1 Regression and Model Building / 1
1.2 Data Collection / 5
1.3 Uses of Regression / 9
1.4 Role of the Computer / 10
2. SIMPLE LINEAR REGRESSION 12
2.1 Simple Linear Regression Model / 12
2.2 Least-Squares Estimation of the Parameters / 13
2.2.1 Estimation of p0 and /3X / 13
2.2.2 Properties of the Least-Squares Estimators
and the Fitted Regression Model /18
2.2.3 Estimation of o2 / 20
2.2.4 Alternate Form of the Model / 22
2.3 Hypothesis Testing on the Slope and Intercept / 22
2.3.1 Use of t Tests / 22
2.3.2 Testing Significance of Regression / 24
2.3.3 Analysis of Variance / 25
2.4 Interval Estimation in Simple Linear Regression / 29
2.4.1 Confidence Intervals on /?0, A and cr / 29
2.4.2 Interval Estimation of the Mean Response / 30
2.5 Prediction of New Observations / 33
2.6 Coefficient of Determination / 35
v
VI
CONTENTS
2.7 A Service Industry Application of Regression / 37
2.8 Using SAS® and R for Simple Linear Regression / 39
2.9 Some Considerations in the Use of Regression / 42
2.10 Regression Through the Origin / 45
2.11 Estimation by Maximum Likelihood / 51
2.12 Case Where the Regressor x is Random / 52
2.12.1 x and y Jointly Distributed / 53
2.12.2 x and y Jointly Normally Distributed:
Correlation Model / 53
Problems / 58
3. MULTIPLE LINEAR REGRESSION
3.1 Multiple Regression Models / 67
3.2 Estimation of the Model Parameters / 70
3.2.1 Least-Squares Estimation of the Regression
Coefficients / 71
3.2.2 Geometrical Interpretation of Least Squares / 77
3.2.3 Properties of the Least-Squares Estimators / 79
3.2.4 Estimation of a2 / 80
3.2.5 Inadequacy of Scatter Diagrams
in Multiple Regression / 82
3.2.6 Maximum-Likelihood Estimation / 83
3.3 Hypothesis Testing in Multiple Linear Regression / 84
3.3.1 Test for Significance of Regression / 84
3.3.2 Tests on Individual Regression Coefficients
and Subsets of Coefficients / 88
3.3.3 Special Case of Orthogonal Columns in X / 93
3.3.4 Testing the General Linear Hypothesis / 95
3.4 Confidence Intervals in Multiple Regression / 97
3.4.1 Confidence Intervals on the Regression Coefficients / 98
3.4.2 Cl Estimation of the Mean Response / 99
3.4.3 Simultaneous Confidence Intervals on Regression
Coefficients / 100
3.5 Prediction of New Observations / 104
3.6 A Multiple Regression Model for the Patient
Satisfaction Data / 104
3.7 Using SAS and R for Basic Multiple Linear Regression / 106
3.8 Hidden Extrapolation in Multiple Regression / 107
3.9 Standardized Regression Coefficients / 111
3.10 Multicollinearity / 117
3.11 Why Do Regression Coefficients Have the Wrong Sign? / 119
Problems I 121
CONTENTS
VII
4. MODEL ADEQUACY CHECKING 129
4.1 Introduction / 129
4.2 Residual Analysis / 130
4.2.1 Definition of Residuals / 130
4.2.2 Methods for Scaling Residuals / 130
4.2.3 Residual Plots / 136
4.2.4 Partial Regression and Partial Residual Plots / 143
4.2.5 Using Minitab®, SAS, and R for Residual Analysis / 146
4.2.6 Other Residual Plotting and Analysis Methods / 149
4.3 PRESS Statistic / 151
4.4 Detection and Treatment of Outliers / 152
4.5 Lack of Fit of the Regression Model / 156
4.5.1 Formal Test for Lack of Fit / 156
4.5.2 Estimation of Pure Error from Near Neighbors / 160
Problems /165
5. TRANSFORMATIONS AND WEIGHTING
TO CORRECT MODEL INADEQUACIES 171
5.1 Introduction / 171
5.2 Variance-Stabilizing Transformations / 172
5.3 Transformations to Linearize the Model / 176
5.4 Analytical Methods for Selecting a Transformation / 182
5.4.1 Transformations on y: The Box-Cox Method / 182
5.4.2 Transformations on the Regressor Variables / 184
5.5 Generalized and Weighted Least Squares / 188
5.5.1 Generalized Least Squares / 188
5.5.2 Weighted Least Squares / 190
5.5.3 Some Practical Issues / 191
5.6 Regression Models with Random Effect / 194
5.6.1 Subsampling / 194
5.6.2 The General Situation for a Regression Model
with a Single Random Effect / 198
5.6.3 The Importance of the Mixed Model in Regression / 202
Problems / 202
6. DIAGNOSTICS FOR LEVERAGE AND INFLUENCE 211
6.1 Importance of Detecting Influential Observations / 211
6.2 Leverage / 212
6.3 Measures of Influence: Cook’s D / 215
6.4 Measures of Influence: DFFITS and DFBETAS / 217
6.5 A Measure of Model Performance / 219
via
CONTENTS
6.6 Detecting Groups of Influential Observations / 220
6.7 Treatment of Influential Observations / 220
Problems / 221
7. POLYNOMIAL REGRESSION MODELS
7.1 Introduction / 223
7.2 Polynomial Models in One Variable / 223
7.2.1 Basic Principles / 223
7.2.2 Piecewise Polynomial Fitting (Splines) / 229
7.2.3 Polynomial and Trigonometric Terms / 235
7.3 Nonparametric Regression / 236
7.3.1 Kernel Regression / 237
7.3.2 Locally Weighted Regression (Loess) / 237
7.3.3 Final Cautions / 241
7.4 Polynomial Models in Two or More Variables i 242
7.5 Orthogonal Polynomials / 248
Problems / 254
8. INDICATOR VARIABLES
8.1 General Concept of Indicator Variables / 260
8.2 Comments on the Use of Indicator Variables / 273
8.2.1 Indicator Variables versus Regression on Allocated
Codes / 273
8.2.2 Indicator Variables as a Substitute for a Quantitative
Regressor / 274
8.3 Regression Approach to Analysis of Variance / 275
Problems / 280
9. MULTICOLL1NEARITY
9.1 Introduction / 285
9.2 Sources of Multicollinearity / 286
9.3 Effects of Multicollinearity / 288
9.4 Multicollinearity Diagnostics / 292
9.4.1 Examination of the Correlation Matrix / 292
9.4.2 Variance Inflation Factors / 296
9.4.3 Eigensystem Analysis of X X / 297
9.4.4 Other Diagnostics / 302
9.4.5 SAS and R Code for Generating Multicollinearity
Diagnostics / 303
9.5 Methods for Dealing with Multicollinearity / 303
9.5.1 Collecting Additional Data / 303
9.5.2 Model Respecification / 304
9.5.3 Ridge Regression / 304
223
260
285
CONTENTS
ix
9.5.4 Principal-Component Regression / 313
9.5.5 Comparison and Evaluation of Biased Estimators / 319
9.6 Using SAS to Perform Ridge and Principal-Component
Regression /321
Problems / 323
10. VARIABLE SELECTION AND MODEL BUILDING
10.1 Introduction / 327
10.1.1 Model-Building Problem / 327
10.1.2 Consequences of Model Misspecification / 329
10.1.3 Criteria for Evaluating Subset Regression Models
10.2 Computational Techniques for Variable Selection / 338
10.2.1 All Possible Regressions / 338
10.2.2 Stepwise Regression Methods / 344
10.3 Strategy for Variable Selection and Model Building / 351
10.4 Case Study: Gorman and Toman Asphalt Data Using SAS
Problems / 367
11. VALIDATION OF REGRESSION MODELS 372
11.1 Introduction / 372
11.2 Validation Techniques / 373
11.2.1 Analysis of Model Coefficients and Predicted Values / 373
11.2.2 Collecting Fresh Data—Confirmation Runs / 375
11.2.3 Data Splitting / 377
11.3 Data from Planned Experiments / 385
Problems / 386
12. INTRODUCTION TO NONLINEAR REGRESSION 389
12.1 Linear and Nonlinear Regression Models / 389
12.1.1 Linear Regression Models / 389
12.2.2 Nonlinear Regression Models / 390
12.2 Origins of Nonlinear Models / 391
12.3 Nonlinear Least Squares / 395
12.4 Transformation to a Linear Model / 397
12.5 Parameter Estimation in a Nonlinear System / 400
12.5.1 Linearization / 400
12.5.2 Other Parameter Estimation Methods / 407
12.5.3 Starting Values / 408
12.6 Statistical Inference in Nonlinear Regression / 409
12.7 Examples of Nonlinear Regression Models /411
12.8 Using SAS and R / 412
Problems / 416
327
/ 332
/ 354
X
CONTENTS
13. GENERALIZED LINEAR MODELS
13.1 Introduction / 421
13.2 Logistic Regression Models / 422
13.2.1 Models with a Binary Response Variable / 422
13.2.2 Estimating the Parameters in a Logistic
Regression Model / 423
13.2.3 Interpretation of the Parameters in
a Logistic Regression Model / 428
13.2.4 Statistical Inference on Model
Parameters / 430
13.2.5 Diagnostic Checking in Logistic
Regression / 440
13.2.6 Other Models for Binary
Response Data / 442
13.2.7 More Than Two Categorical Outcomes / 442
13.3 Poisson Regression / 444
13.4 The Generalized Linear Model / 450
13.4.1 Link Functions and Linear Predictors / 451
13.4.2 Parameter Estimation and Inference
in the GLM / 452
13.4.3 Prediction and Estimation with the GLM / 454
13.4.4 Residual Analysis in the GLM / 456
13.4.5 Using R to Perform GLM Analysis / 458
13.4.6 Overdispersion / 461
Problems / 462
14. REGRESSION ANALYSIS OF TIME SERIES DATA
14.1 Introduction to Regression Models for
Time Series Data / 474
14.2 Detecting Autocorrelation: The Durbin-Watson
Test / 475
14.3 Estimating the Parameters in Time Series Regression
Models / 480
Problems / 496
15. OTHER TOPICS IN THE USE OF REGRESSION ANALYSIS
15.1 Robust Regression / 500
15.1.1 Need for Robust Regression / 500
15.1.2 M~Estimators / 503
15.1.3 Properties of Robust Estimators / 510
CONTENTS
хі
15.2 Effect of Measurement Errors in the Regressors / 511
15.2.1 Simple Linear Regression / 511
15.2.2 The Berkson Model / 513
15.3 Inverse Estimation—The Calibration Problem / 513
15.4 Bootstrapping in Regression / 517
15.4.1 Bootstrap Sampling in Regression / 518
15.4.2 Bootstrap Confidence Intervals / 519
15.5 Classification and Regression Trees (CART) / 524
15.6 Neural Networks / 526
15.7 Designed Experiments for Regression / 529
Problems / 537
APPENDIX A. STATISTICAL TABLES 541
APPENDIX B. DATA SETS FOR EXERCISES 553
APPENDIX C. SUPPLEMENTAL TECHNICAL MATERIAL 574
C.l Background on Basic Test Statistics / 574
C.2 Background from the Theory of Linear Models / 577
C.3 Important Results on SSR and SSRes / 581
C.4 Gauss-Markov Theorem, Var(e) = tT / 587
C.5 Computational Aspects of Multiple Regression / 589
C6 Result on the Inverse of a Matrix / 590
C.7 Development of the PRESS Statistic / 591
C.8 Development of Sfc) / 593
C.9 Outlier Test Based on Я-Student / 594
C.10 Independence of Residuals and Fitted Values / 596
C.ll Gauss-Markov Theorem, Var(e) = V / 597
C.12 Bias in MSRes When the Model Is Underspecified / 599
C.13 Computation of Influence Diagnostics і 600
C. 14 Generalized Linear Models / 601
APPENDIX D. INTRODUCTION TO SAS 613
D. l Basic Data Entry / 614
D.2 Creating Permanent SAS Data Sets l 618
D.3 Importing Data from an EXCEL File / 619
D.4 Output Command / 620
D.5 Log File / 620
D.6 Adding Variables to an Existing SAS Data Set / 622
xii CONTENTS
APPENDIX E. INTRODUCTION TO R TO PERFORM LINEAR
REGRESSION ANALYSIS
E.l Basic Background on R / 623
E.2 Basic Data Entry / 624
E.3 Brief Comments on Other Functionality in R / 626
E.4 R Commander / 627
623
REFERENCES
INDEX
628
642
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.536 |
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| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spellingShingle | Montgomery, Douglas C. 1943- Peck, Elizabeth A. 1953- Vining, G. Geoffrey 1954- Introduction to linear 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 ; 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 | Lineare Regression (DE-588)4167709-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| topic_facet | Lineare Regression Regressionsanalyse Lineares Regressionsmodell Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021211686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT montgomerydouglasc introductiontolinearregressionanalysis AT peckelizabetha introductiontolinearregressionanalysis AT viningggeoffrey introductiontolinearregressionanalysis |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 628f 2001 A 25449(5)
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
Teilbibliothek Physik
| Signatur: |
0202 MAT 628f 2012 B 1684(5)
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |