Regression analysis by example:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2006
|
| Edition: | 4. ed. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 375 S. graph. Darst. |
| ISBN: | 0471746967 9780471746966 |
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| adam_text | Titel: Regression analysis by example
Autor: Chatterjee, Samprit
Jahr: 2006
CONTENTS
Preface xiii
Introduction 1
1.1 What Is Regression Analysis? 1
1.2 Publicly Available Data Sets 2
1.3 Selected Applications of Regression Analysis 3
1.3.1 Agricultural Sciences 3
1.3.2 Industrial and Labor Relations 3
1.3.3 History 4
1.3.4 Government 6
1.3.5 Environmental Sciences 6
1.4 Steps in Regression Analysis 7
1.4.1 Statement of the Problem 11
1.4.2 Selection of Potentially Relevant Variables 11
1.4.3 Data Collection 11
1.4.4 Model Specification 12
1.4.5 Method of Fitting 14
1.4.6 Model Fitting 14
1.4.7 Model Criticism and Selection 16
1.4.8 Objectives of Regression Analysis 16
1.5 Scope and Organization of the Book 17
Exercises 18
CONTENTS
Simple Linear Regression 21
2.1 Introduction 21
2.2 Covariance and Correlation Coefficient 21
2.3 Example: Computer Repair Data 26
2.4 The Simple Linear Regression Model 28
2.5 Parameter Estimation 29
2.6 Tests of Hypotheses 32
2.7 Confidence Intervals 37
2.8 Predictions 37
2.9 Measuring the Quality of Fit 39
2.10 Regression Line Through the Origin 42
2.11 Trivial Regression Models 44
2.12 Bibliographic Notes 45
Exercises 45
Multiple Linear Regression 53
3.1 Introduction 53
3.2 Description of the Data and Model 53
3.3 Example: Supervisor Performance Data 54
3.4 Parameter Estimation 57
3.5 Interpretations of Regression Coefficients 58
3.6 Properties of the Least Squares Estimators 60
3.7 Multiple Correlation Coefficient 61
3.8 Inference for Individual Regression Coefficients 62
3.9 Tests of Hypotheses in a Linear Model 64
3.9.1 Testing All Regression Coefficients Equal to Zero 66
3.9.2 Testing a Subset of Regression Coefficients Equal to
Zero 69
3.9.3 Testing the Equality of Regression Coefficients 71
3.9.4 Estimating and Testing of Regression Parameters
Under Constraints 73
3.10 Predictions 74
3.11 Summary 75
Exercises 75
Appendix: Multiple Regression in Matrix Notation 82
Regression Diagnostics: Detection of Model Violations 85
4.1 Introduction 85
4.2 The Standard Regression Assumptions 86
4.3 Various Types of Residuals 88
4.4 Graphical Methods 90
4.5 Graphs Before Fitting a Model 93
CONTENTS IX
4.5.1 One-Dimensional Graphs 93
4.5.2 Two-Dimensional Graphs 93
4.5.3 Rotating Plots 96
4.5.4 Dynamic Graphs 96
4.6 Graphs After Fitting a Model 97
4.7 Checking Linearity and Normality Assumptions 97
4.8 Leverage, Influence, and Outliers 98
4.8.1 Outliers in the Response Variable 100
4.8.2 Outliers in the Predictors 100
4.8.3 Masking and Swamping Problems 100
4.9 Measures of Influence 103
4.9.1 Cook s Distance 103
4.9.2 Welsch and Kuh Measure 104
4.9.3 Hadi s influence Measure 105
4.10 The Potential-Residual Plot 107
4.11 What to Do with the Outliers? 108
4.12 Role of Variables in a Regression Equation 109
4.12.1 Added-Variable Plot 109
4.12.2 Residual Plus Component Plot 110
4.13 Effects of an Additional Predictor 114
4.14 Robust Regression 115
Exercises 115
Qualitative Variables as Predictors 121
5.1 Introduction 121
5.2 Salary Survey Data 122
5.3 Interaction Variables 125
5.4 Systems of Regression Equations 128
5.4.1 Models with Different Slopes and Different Intercepts 130
5.4.2 Models with Same Slope and Different Intercepts 137
5.4.3 Models with Same Intercept and Different Slopes 138
5.5 Other Applications of Indicator Variables 139
5.6 Seasonality 140
5.7 Stability of Regression Parameters Over Time 141
Exercises 143
Transformation of Variables 151
6.1 Introduction 151
6.2 Transformations to Achieve Linearity 153
6.3 Bacteria Deaths Due to X-Ray Radiation 155
6.3.1 Inadequacy of a Linear Model 156
6.3.2 Logarithmic Transformation for Achieving Linearity 158
X CONTENTS
6.4 Transformations to Stabilize Variance 159
6.5 Detection of Heteroscedastic Errors 164
6.6 Removal of Heteroscedasticity 166
6.7 Weighted Least Squares 167
6.8 Logarithmic Transformation of Data 168
6.9 Power Transformation 169
6.10 Summary 173
Exercises 174
7 Weighted Least Squares 179
7.1 Introduction 179
7.2 Heteroscedastic Models 180
7.2.1 Supervisors Data 180
7.2.2 College Expense Data 182
7.3 Two-Stage Estimation 183
7.4 Education Expenditure Data 185
7.5 Fitting a Dose-Response Relationship Curve 194
Exercises 196
8 The Problem of Correlated Errors 197
8.1 Introduction: Autocorrelation 197
8.2 Consumer Expenditure and Money Stock 198
8.3 Durbin-Watson Statistic 200
8.4 Removal of Autocorrelation by Transformation 202
8.5 Iterative Estimation With Autocorrelated Errors 204
8.6 Autocorrelation and Missing Variables 205
8.7 Analysis of Housing Starts 206
8.8 Limitations of Durbin-Watson Statistic 210
8.9 Indicator Variables to Remove Seasonality 211
8.10 Regressing Two Time Series 214
Exercises 216
9 Analysis of Collinear Data 221
9.1 Introduction 221
9.2 Effects on Inference 222
9.3 Effects on Forecasting 228
9.4 Detection of Multicollinearity 233
9.5 Centering and Scaling 239
9.5.1 Centering and Scaling in Intercept Models 240
9.5.2 Scaling in No-Intercept Models 241
9.6 Principal Components Approach 243
9.7 Imposing Constraints 246
CONTENTS Xl
9.8 Searching for Linear Functions of the ß s 248
9.9 Computations Using Principal Components 252
9.10 Bibliographic Notes 254
Exercises 254
Appendix: Principal Components 255
10 Biased Estimation of Regression Coefficients 259
10.1 Introduction 259
10.2 Principal Components Regression 260
10.3 Removing Dependence Among the Predictors 262
10.4 Constraints on the Regression Coefficients 264
10.5 Principal Components Regression: A Caution 265
10.6 Ridge Regression 268
10.7 Estimation by the Ridge Method 269
10.8 Ridge Regression: Some Remarks 272
10.9 Summary 275
Exercises 275
Appendix: Ridge Regression 277
11 Variable Selection Procedures 281
11.1 Introduction 281
11.2 Formulation of the Problem 282
11.3 Consequences of Variables Deletion 282
11.4 Uses of Regression Equations 284
11.4.1 Description and Model Building 284
11.4.2 Estimation and Prediction 284
11.4.3 Control 284
11.5 Criteria for Evaluating Equations 285
11.5.1 Residual Mean Square 285
11.5.2 Mallows Cp 286
11.5.3 Information Criteria: Akaike and Other Modified
Forms 287
11.6 Multicollinearity and Variable Selection 288
11.7 Evaluating All Possible Equations 288
11.8 Variable Selection Procedures 289
11.8.1 Forward Selection Procedure 289
11.8.2 Backward Elimination Procedure 290
11.8.3 Stepwise Method 290
11.9 General Remarks on Variable Selection Methods 291
11.10 A Study of Supervisor Performance 292
11.11 Variable Selection With Collinear Data 296
11.12 The Homicide Data 296
XII CONTENTS
11.13 Variable Selection Using Ridge Regression 299
11.14 Selection of Variables in an Air Pollution Study 300
11.15 A Possible Strategy for Fitting Regression Models 307
11.16 Bibliographic Notes 308
Exercises 308
Appendix: Effects of Incorrect Model Specifications 313
12 Logistic Regression 317
12.1 Introduction 317
12.2 Modeling Qualitative Data 318
12.3 The Logit Model 318
12.4 Example: Estimating Probability of Bankruptcies 320
12.5 Logistic Regression Diagnostics 323
12.6 Determination of Variables to Retain 324
12.7 Judging the Fit of a Logistic Regression 327
12.8 The Multinomial Logit Model 329
12.8.1 Multinomial Logistic Regression 329
12.8.2 Example: Determining Chemical Diabetes 330
12.8.3 Ordered Response Category: Ordinal Logistic
Regression 334
12.8.4 Example: Determining Chemical Diabetes Revisited 335
12.9 Classification Problem: Another Approach 336
Exercises 337
13 Further Topics 341
13.1 Introduction 341
13.2 Generalized Linear Model 341
13.3 Poisson Regression Model 342
13.4 Introduction of New Drugs 343
13.5 Robust Regression 345
13.6 Fitting a Quadratic Model 346
13.7 Distribution of PCB in U.S. Bays 348
Exercises 352
Appendix A: Statistical Tables 353
References 353
Index
371
|
| adam_txt |
Titel: Regression analysis by example
Autor: Chatterjee, Samprit
Jahr: 2006
CONTENTS
Preface xiii
Introduction 1
1.1 What Is Regression Analysis? 1
1.2 Publicly Available Data Sets 2
1.3 Selected Applications of Regression Analysis 3
1.3.1 Agricultural Sciences 3
1.3.2 Industrial and Labor Relations 3
1.3.3 History 4
1.3.4 Government 6
1.3.5 Environmental Sciences 6
1.4 Steps in Regression Analysis 7
1.4.1 Statement of the Problem 11
1.4.2 Selection of Potentially Relevant Variables 11
1.4.3 Data Collection 11
1.4.4 Model Specification 12
1.4.5 Method of Fitting 14
1.4.6 Model Fitting 14
1.4.7 Model Criticism and Selection 16
1.4.8 Objectives of Regression Analysis 16
1.5 Scope and Organization of the Book 17
Exercises 18
CONTENTS
Simple Linear Regression 21
2.1 Introduction 21
2.2 Covariance and Correlation Coefficient 21
2.3 Example: Computer Repair Data 26
2.4 The Simple Linear Regression Model 28
2.5 Parameter Estimation 29
2.6 Tests of Hypotheses 32
2.7 Confidence Intervals 37
2.8 Predictions 37
2.9 Measuring the Quality of Fit 39
2.10 Regression Line Through the Origin 42
2.11 Trivial Regression Models 44
2.12 Bibliographic Notes 45
Exercises 45
Multiple Linear Regression 53
3.1 Introduction 53
3.2 Description of the Data and Model 53
3.3 Example: Supervisor Performance Data 54
3.4 Parameter Estimation 57
3.5 Interpretations of Regression Coefficients 58
3.6 Properties of the Least Squares Estimators 60
3.7 Multiple Correlation Coefficient 61
3.8 Inference for Individual Regression Coefficients 62
3.9 Tests of Hypotheses in a Linear Model 64
3.9.1 Testing All Regression Coefficients Equal to Zero 66
3.9.2 Testing a Subset of Regression Coefficients Equal to
Zero 69
3.9.3 Testing the Equality of Regression Coefficients 71
3.9.4 Estimating and Testing of Regression Parameters
Under Constraints 73
3.10 Predictions 74
3.11 Summary 75
Exercises 75
Appendix: Multiple Regression in Matrix Notation 82
Regression Diagnostics: Detection of Model Violations 85
4.1 Introduction 85
4.2 The Standard Regression Assumptions 86
4.3 Various Types of Residuals 88
4.4 Graphical Methods 90
4.5 Graphs Before Fitting a Model 93
CONTENTS IX
4.5.1 One-Dimensional Graphs 93
4.5.2 Two-Dimensional Graphs 93
4.5.3 Rotating Plots 96
4.5.4 Dynamic Graphs 96
4.6 Graphs After Fitting a Model 97
4.7 Checking Linearity and Normality Assumptions 97
4.8 Leverage, Influence, and Outliers 98
4.8.1 Outliers in the Response Variable 100
4.8.2 Outliers in the Predictors 100
4.8.3 Masking and Swamping Problems 100
4.9 Measures of Influence 103
4.9.1 Cook's Distance 103
4.9.2 Welsch and Kuh Measure 104
4.9.3 Hadi's influence Measure 105
4.10 The Potential-Residual Plot 107
4.11 What to Do with the Outliers? 108
4.12 Role of Variables in a Regression Equation 109
4.12.1 Added-Variable Plot 109
4.12.2 Residual Plus Component Plot 110
4.13 Effects of an Additional Predictor 114
4.14 Robust Regression 115
Exercises 115
Qualitative Variables as Predictors 121
5.1 Introduction 121
5.2 Salary Survey Data 122
5.3 Interaction Variables 125
5.4 Systems of Regression Equations 128
5.4.1 Models with Different Slopes and Different Intercepts 130
5.4.2 Models with Same Slope and Different Intercepts 137
5.4.3 Models with Same Intercept and Different Slopes 138
5.5 Other Applications of Indicator Variables 139
5.6 Seasonality 140
5.7 Stability of Regression Parameters Over Time 141
Exercises 143
Transformation of Variables 151
6.1 Introduction 151
6.2 Transformations to Achieve Linearity 153
6.3 Bacteria Deaths Due to X-Ray Radiation 155
6.3.1 Inadequacy of a Linear Model 156
6.3.2 Logarithmic Transformation for Achieving Linearity 158
X CONTENTS
6.4 Transformations to Stabilize Variance 159
6.5 Detection of Heteroscedastic Errors 164
6.6 Removal of Heteroscedasticity 166
6.7 Weighted Least Squares 167
6.8 Logarithmic Transformation of Data 168
6.9 Power Transformation 169
6.10 Summary 173
Exercises 174
7 Weighted Least Squares 179
7.1 Introduction 179
7.2 Heteroscedastic Models 180
7.2.1 Supervisors Data 180
7.2.2 College Expense Data 182
7.3 Two-Stage Estimation 183
7.4 Education Expenditure Data 185
7.5 Fitting a Dose-Response Relationship Curve 194
Exercises 196
8 The Problem of Correlated Errors 197
8.1 Introduction: Autocorrelation 197
8.2 Consumer Expenditure and Money Stock 198
8.3 Durbin-Watson Statistic 200
8.4 Removal of Autocorrelation by Transformation 202
8.5 Iterative Estimation With Autocorrelated Errors 204
8.6 Autocorrelation and Missing Variables 205
8.7 Analysis of Housing Starts 206
8.8 Limitations of Durbin-Watson Statistic 210
8.9 Indicator Variables to Remove Seasonality 211
8.10 Regressing Two Time Series 214
Exercises 216
9 Analysis of Collinear Data 221
9.1 Introduction 221
9.2 Effects on Inference 222
9.3 Effects on Forecasting 228
9.4 Detection of Multicollinearity 233
9.5 Centering and Scaling 239
9.5.1 Centering and Scaling in Intercept Models 240
9.5.2 Scaling in No-Intercept Models 241
9.6 Principal Components Approach 243
9.7 Imposing Constraints 246
CONTENTS Xl
9.8 Searching for Linear Functions of the ß's 248
9.9 Computations Using Principal Components 252
9.10 Bibliographic Notes 254
Exercises 254
Appendix: Principal Components 255
10 Biased Estimation of Regression Coefficients 259
10.1 Introduction 259
10.2 Principal Components Regression 260
10.3 Removing Dependence Among the Predictors 262
10.4 Constraints on the Regression Coefficients 264
10.5 Principal Components Regression: A Caution 265
10.6 Ridge Regression 268
10.7 Estimation by the Ridge Method 269
10.8 Ridge Regression: Some Remarks 272
10.9 Summary 275
Exercises 275
Appendix: Ridge Regression 277
11 Variable Selection Procedures 281
11.1 Introduction 281
11.2 Formulation of the Problem 282
11.3 Consequences of Variables Deletion 282
11.4 Uses of Regression Equations 284
11.4.1 Description and Model Building 284
11.4.2 Estimation and Prediction 284
11.4.3 Control 284
11.5 Criteria for Evaluating Equations 285
11.5.1 Residual Mean Square 285
11.5.2 Mallows Cp 286
11.5.3 Information Criteria: Akaike and Other Modified
Forms 287
11.6 Multicollinearity and Variable Selection 288
11.7 Evaluating All Possible Equations 288
11.8 Variable Selection Procedures 289
11.8.1 Forward Selection Procedure 289
11.8.2 Backward Elimination Procedure 290
11.8.3 Stepwise Method 290
11.9 General Remarks on Variable Selection Methods 291
11.10 A Study of Supervisor Performance 292
11.11 Variable Selection With Collinear Data 296
11.12 The Homicide Data 296
XII CONTENTS
11.13 Variable Selection Using Ridge Regression 299
11.14 Selection of Variables in an Air Pollution Study 300
11.15 A Possible Strategy for Fitting Regression Models 307
11.16 Bibliographic Notes 308
Exercises 308
Appendix: Effects of Incorrect Model Specifications 313
12 Logistic Regression 317
12.1 Introduction 317
12.2 Modeling Qualitative Data 318
12.3 The Logit Model 318
12.4 Example: Estimating Probability of Bankruptcies 320
12.5 Logistic Regression Diagnostics 323
12.6 Determination of Variables to Retain 324
12.7 Judging the Fit of a Logistic Regression 327
12.8 The Multinomial Logit Model 329
12.8.1 Multinomial Logistic Regression 329
12.8.2 Example: Determining Chemical Diabetes 330
12.8.3 Ordered Response Category: Ordinal Logistic
Regression 334
12.8.4 Example: Determining Chemical Diabetes Revisited 335
12.9 Classification Problem: Another Approach 336
Exercises 337
13 Further Topics 341
13.1 Introduction 341
13.2 Generalized Linear Model 341
13.3 Poisson Regression Model 342
13.4 Introduction of New Drugs 343
13.5 Robust Regression 345
13.6 Fitting a Quadratic Model 346
13.7 Distribution of PCB in U.S. Bays 348
Exercises 352
Appendix A: Statistical Tables 353
References 353
Index
371 |
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| author | Chatterjee, Samprit 1938- Hadi, Ali S. |
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| dewey-full | 519.5/36 |
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| dewey-raw | 519.5/36 |
| dewey-search | 519.5/36 |
| dewey-sort | 3519.5 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Einführung Lehrbuch |
| id | DE-604.BV021734626 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:27:30Z |
| indexdate | 2024-07-09T20:42:48Z |
| institution | BVB |
| isbn | 0471746967 9780471746966 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014948087 |
| oclc_num | 66527281 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-11 DE-188 DE-824 DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-11 DE-188 DE-824 DE-83 |
| physical | XV, 375 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Chatterjee, Samprit 1938- Verfasser (DE-588)172018978 aut Regression analysis by example Samprit Chatterjee ; Ali S. Hadi 4. ed. Hoboken, NJ Wiley 2006 XV, 375 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Analyse de régression Analyse de régression ram Statistique ram Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Regressionsanalyse (DE-588)4129903-6 s Anwendung (DE-588)4196864-5 s 3\p DE-604 Statistik (DE-588)4056995-0 s 4\p DE-604 Hadi, Ali S. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014948087&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chatterjee, Samprit 1938- Hadi, Ali S. Regression analysis by example Analyse de régression Analyse de régression ram Statistique ram Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Anwendung (DE-588)4196864-5 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4196864-5 (DE-588)4056995-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Regression analysis by example |
| title_auth | Regression analysis by example |
| title_exact_search | Regression analysis by example |
| title_exact_search_txtP | Regression analysis by example |
| title_full | Regression analysis by example Samprit Chatterjee ; Ali S. Hadi |
| title_fullStr | Regression analysis by example Samprit Chatterjee ; Ali S. Hadi |
| title_full_unstemmed | Regression analysis by example Samprit Chatterjee ; Ali S. Hadi |
| title_short | Regression analysis by example |
| title_sort | regression analysis by example |
| topic | Analyse de régression Analyse de régression ram Statistique ram Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Anwendung (DE-588)4196864-5 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Analyse de régression Statistique Regression analysis Regressionsanalyse Anwendung Statistik Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014948087&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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