Applied linear regression:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken
Wiley
[2014]
|
| Edition: | Fourth Edition |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 340 Seiten Diagramme |
| ISBN: | 9781118386088 |
Staff View
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Record in the Search Index
| _version_ | 1804151830681223168 |
|---|---|
| adam_text | Titel: Applied linear regression
Autor: Weisberg, Sanford
Jahr: 2014
Contents
Preface to the Fourth Edition
1 Scatterplots and Regression
1.1 Scatterplots, 2
1.2 Mean Functions, 10
1.3 Variance Functions, 12
1.4 Summary Graph, 12
1.5 Tools for Looking at Scatterplots, 13
1.5.1 Size, 14
1.5.2 Transformations, 14
1.5.3 Smoothers for the Mean Function, 14
1.6 Scatterplot Matrices, 15
1.7 Problems, 17
2 Simple Linear Regression
2.1 Ordinary Least Squares Estimation, 22
2.2 Least Squares Criterion, 24
2.3 Estimating the Variance a2, 26
2.4 Properties of Least Squares Estimates, 27
2.5 Estimated Variances, 29
2.6 Confidence Intervals and i-Tests, 30
2.6.1 The Intercept, 30
2.6.2 Slope, 31
2.6.3 Prediction, 32
2.6.4 Fitted Values, 33
2.7 The Coefficient of Determination, R2, 35
2.8 The Residuals, 36
2.9 Problems, 38
viii
CONTENTS
3 Multiple Regression 51
3.1 Adding a Regressor to a Simple Linear Regression
Model, 51
3.1.1 Explaining Variability, 53
3.1.2 Added-Variable Plots, 53
3.2 The Multiple Linear Regression Model, 55
3.3 Predictors and Regressors, 55
3.4 Ordinary Least Squares, 58
3.4.1 Data and Matrix Notation, 60
3.4.2 The Errors e, 61
3.4.3 Ordinary Least Squares Estimators, 61
3.4.4 Properties of the Estimates, 63
3.4.5 Simple Regression in Matrix
Notation, 63
3.4.6 The Coefficient of Determination, 66
3.4.7 Hypotheses Concerning One
Coefficient, 67
3.4.8 f-Tests and Added-Variable Plots, 68
3.5 Predictions, Fitted Values, and Linear
Combinations, 68
3.6 Problems, 69
4 Interpretation of Main Effects 73
4.1 Understanding Parameter Estimates, 73
4.1.1 Rate of Change, 74
4.1.2 Signs of Estimates, 75
4.1.3 Interpretation Depends on Other Terms in
the Mean Function, 75
4.1.4 Rank Deficient and Overparameterized Mean
Functions, 78
4.1.5 Collinearity, 79
4.1.6 Regressors in Logarithmic Scale, 81
4.1.7 Response in Logarithmic Scale, 82
4.2 Dropping Regressors, 84
4.2.1 Parameters, 84
4.2.2 Variances, 86
4.3 Experimentation versus Observation, 86
4.3.1 Feedlots, 87
4.4 Sampling from a Normal Population, 89
CONTENTS
ix
4.5 More on R2, 91
4.5.1 Simple Linear Regression and R2, 91
4.5.2 Multiple Linear Regression and R2, 92
4.5.3 Regression through the Origin, 93
4.6 Problems, 93
5 Complex Regressors 98
5.1 Factors, 98
5.1.1 One-Factor Models, 99
5.1.2 Comparison of Level Means, 102
5.1.3 Adding a Continuous Predictor, 103
5.1.4 The Main Effects Model, 106
5.2 Many Factors, 108
5.3 Polynomial Regression, 109
5.3.1 Polynomials with Several Predictors, 111
5.3.2 Numerical Issues with Polynomials, 112
5.4 Splines, 113
5.4.1 Choosing a Spline Basis, 115
5.4.2 Coefficient Estimates, 116
5.5 Principal Components, 116
5.5.1 Using Principal Components, 118
5.5.2 Scaling, 119
5.6 Missing Data, 119
5.6.1 Missing at Random, 120
5.6.2 Imputation, 122
5.7 Problems, 123
6 Testing and Analysis of Variance 133
6.1 F-Tests, 134
6.1.1 General Likelihood Ratio Tests, 138
6.2 The Analysis of Variance, 138
6.3 Comparisons of Means, 142
6.4 Power and Non-Null Distributions, 143
6.5 Wald Tests, 145
6.5.1 One Coefficient, 145
6.5.2 One Linear Combination, 146
6.5.3 General Linear Hypothesis, 146
6.5.4 Equivalence of Wald and Likelihood-Ratio
Tests, 146
X
CONTENTS
6.6 Interpreting Tests, 146
6.6.1 Interpreting /^-Values, 146
6.6.2 Why Most Published Research Findings
Are False, 147
6.6.3 Look at the Data, Not Just the Tests, 148
6.6.4 Population versus Sample, 149
6.6.5 Stacking the Deck, 149
6.6.6 Multiple Testing, 150
6.6.7 File Drawer Effects, 150
6.6.8 The Lab Is Not the Real World, 150
6.7 Problems, 150
7 Variances 156
7.1 Weighted Least Squares, 156
7.1.1 Weighting of Group Means, 159
7.1.2 Sample Surveys, 161
7.2 Misspecified Variances, 162
7.2.1 Accommodating Misspecified Variance, 163
7.2.2 A Test for Constant Variance, 164
7.3 General Correlation Structures, 168
7.4 Mixed Models, 169
7.5 Variance Stabilizing Transformations, 171
7.6 The Delta Method, 172
7.7 The Bootstrap, 174
7.7.1 Regression Inference without Normality, 175
7.7.2 Nonlinear Functions of Parameters, 178
7.7.3 Residual Bootstrap, 179
7.7.4 Bootstrap Tests, 179
7.8 Problems, 179
8 Transformations 185
8.1 Transformation Basics, 185
8.1.1 Power Transformations, 186
8.1.2 Transforming One Predictor Variable, 188
8.1.3 The Box-Cox Method, 190
8.2 A General Approach to Transformations, 191
8.2.1 The ID Estimation Result and Linearly Related
Regressors, 194
8.2.2 Automatic Choice of Transformation of
Predictors, 195
CONTENTS
8.3 Transforming the Response, 196
8.4 Transformations of Nonpositive Variables, 198
8.5 Additive Models, 199
8.6 Problems, 199
9 Regression Diagnostics
9.1 The Residuals, 204
9.1.1 Difference between ê and e, 205
9.1.2 The Hat Matrix, 206
9.1.3 Residuals and the Hat Matrix with Weights, 208
9.1.4 Residual Plots When the Model Is Correct, 209
9.1.5 The Residuals When the Model Is Not
Correct, 209
9.1.6 Fuel Consumption Data, 211
9.2 Testing for Curvature, 212
9.3 Nonconstant Variance, 213
9.4 Outliers, 214
9.4.1 An Outlier Test, 215
9.4.2 Weighted Least Squares, 216
9.4.3 Significance Levels for the Outlier Test, 217
9.4.4 Additional Comments, 218
9.5 Influence of Cases, 218
9.5.1 Cook s Distance, 220
9.5.2 Magnitude of D„ 221
9.5.3 Computing D¡, 221
9.5.4 Other Measures of Influence, 224
9.6 Normality Assumption, 225
9.7 Problems, 226
10 Variable Selection
10.1 Variable Selection and Parameter Assessment, 235
10.2 Variable Selection for Discovery, 237
10.2.1 Information Criteria, 238
10.2.2 Stepwise Regression, 239
10.2.3 Regularized Methods, 244
10.2.4 Subset Selection Overstates Significance, 245
10.3 Model Selection for Prediction, 245
10.3.1 Cross-Validation, 247
10.3.2 Professor Ratings, 247
10.4 Problems, 248
11 Nonlinear Regression
11.1 Estimation for Nonlinear Mean Functions, 253
11.2 Inference Assuming Large Samples, 256
11.3 Starting Values, 257
11.4 Bootstrap Inference, 262
11.5 Further Reading, 265
11.6 Problems, 265
12 Binomial and Poisson Regression
12.1 Distributions for Counted Data, 270
12.1.1 Bernoulli Distribution, 270
12.1.2 Binomial Distribution, 271
12.1.3 Poisson Distribution, 271
12.2 Regression Models for Counts, 272
12.2.1 Binomial Regression, 272
12.2.2 Deviance, 277
12.3 Poisson Regression, 279
12.3.1 Goodness of Fit Tests, 282
12.4 Transferring What You Know about Linear Models, 283
12.4.1 Scatterplots and Regression, 283
12.4.2 Simple and Multiple Regression, 283
12.4.3 Model Building, 284
12.4.4 Testing and Analysis of Deviance, 284
12.4.5 Variances, 284
12.4.6 Transformations, 284
12.4.7 Regression Diagnostics, 284
12.4.8 Variable Selection, 285
12.5 Generalized Linear Models, 285
12.6 Problems, 285
Appendix
A.l Website, 290
A.2 Means, Variances, Covariances, and Correlations, 290
A.2.1 The Population Mean and E Notation, 290
A.2.2 Variance and Var Notation, 291
A.2.3 Covariance and Correlation, 291
A.2.4 Conditional Moments, 292
A.3 Least Squares for Simple Regression, 293
CONTENTS
xiii
A.4 Means and Variances of Least Squares Estimates, 294
A.5 Estimating E(Y X) Using a Smoother, 296
A.6 A Brief Introduction to Matrices and Vectors, 298
A.6.1 Addition and Subtraction, 299
A.6.2 Multiplication by a Scalar, 299
A.6.3 Matrix Multiplication, 299
A.6.4 Transpose of a Matrix, 300
A.6.5 Inverse of a Matrix, 301
A.6.6 Orthogonality, 302
A.6.7 Linear Dependence and Rank of a Matrix, 303
A.7 Random Vectors, 303
A.8 Least Squares Using Matrices, 304
A.8.1 Properties of Estimates, 305
A.8.2 The Residual Sum of Squares, 305
A.8.3 Estimate of Variance, 306
A.8.4 Weighted Least Squares, 306
A.9 The QR Factorization, 307
A.10 Spectral Decomposition, 309
A. 11 Maximum Likelihood Estimates, 309
A.11.1 Linear Models, 309
A.11.2 Logistic Regression, 311
A.12 The Box-Cox Method for Transformations, 312
A.12.1 Univariate Case, 312
A.12.2 Multivariate Case, 313
A.13 Case Deletion in Linear Regression, 314
References 317
Author Index 329
Subject Index 331
|
| any_adam_object | 1 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5/36 19 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Weisberg, Sanford 1947- Verfasser (DE-588)170214664 aut Applied linear regression Sanford Weisberg, School of Statistics, University of Minnesota, Minneapolis, MN Fourth Edition Hoboken Wiley [2014] xvii, 340 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Regression analysis Statistik (DE-588)4056995-0 gnd rswk-swf Lineare Regression (DE-588)4167709-2 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Statistik (DE-588)4056995-0 s 1\p DE-604 Lineare Regression (DE-588)4167709-2 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027061185&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 |
| spellingShingle | Weisberg, Sanford 1947- Applied linear regression Regression analysis Statistik (DE-588)4056995-0 gnd Lineare Regression (DE-588)4167709-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4167709-2 (DE-588)4129903-6 |
| title | Applied linear regression |
| title_auth | Applied linear regression |
| title_exact_search | Applied linear regression |
| title_full | Applied linear regression Sanford Weisberg, School of Statistics, University of Minnesota, Minneapolis, MN |
| title_fullStr | Applied linear regression Sanford Weisberg, School of Statistics, University of Minnesota, Minneapolis, MN |
| title_full_unstemmed | Applied linear regression Sanford Weisberg, School of Statistics, University of Minnesota, Minneapolis, MN |
| title_short | Applied linear regression |
| title_sort | applied linear regression |
| topic | Regression analysis Statistik (DE-588)4056995-0 gnd Lineare Regression (DE-588)4167709-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Regression analysis Statistik Lineare Regression Regressionsanalyse |
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