A modern approach to regression with R:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
[2009]
|
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 392 Seiten Illustrationen |
| ISBN: | 9780387096070 |
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| 100 | 1 | |a Sheather, Simon J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A modern approach to regression with R |c Simon J. Sheather |
| 264 | 1 | |a New York, NY |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a XIV, 392 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer texts in statistics | |
| 650 | 4 | |a Analyse de régression | |
| 650 | 4 | |a R (Langage de programmation) | |
| 650 | 7 | |a R (computerprogramma) |2 gtt | |
| 650 | 7 | |a Regressieanalyse |2 gtt | |
| 650 | 4 | |a R (Computer program language) | |
| 650 | 4 | |a Regression analysis | |
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Contents
1
Introduction
. 1
1.1 Building
Valid
Models. 1
1.2
Motivating Examples
. 1
1.2.1
Assessing the Ability of NFL Kickers
. 1
1.2.2
Newspaper Circulation
. 4
1.2.3
Menu Pricing in a New Italian Restaurant
in New York City
. 5
1.2.4
Effect of Wine Critics' Ratings on Prices
of Bordeaux Wines
. 8
1.3
Level of Mathematics
. 13
2
Simple Linear Regression
. 15
2.1
Introduction and Least Squares Estimates
. 15
2.1.1
Simple Linear Regression Models
. 15
2.2
Inferences About the Slope and the Intercept
. 20
2.2.1
Assumptions Necessary in Order to Make Inferences
About the Regression Model
. 21
2.2.2
Inferences About the Slope of the Regression Line
. 21
2.2.3
Inferences About the Intercept of the Regression Line
. 23
2.3
Confidence Intervals for the Population Regression Line
. 24
2.4
Prediction Intervals for the Actual Value of
Y
. 25
2.5
Analysis of Variance
. 27
2.6
Dummy Variable Regression
. 30
2.7
Derivations of Results
. 33
2.7.1
Inferences about the Slope of the Regression Line
. 34
2.7.2
Inferences about the Intercept of the Regression Line
. 35
2.7.3
Confidence Intervals for the Population Regression Line
. 36
2.7.4
Prediction Intervals for the Actual Value of
Y
. 37
2.8
Exercises
. 38
xii Contents
3
Diagnostics and Transformations for Simple
Linear Regression
. 45
3.1
Valid and Invalid Regression Models:
Anscombe's Four Data Sets
. 45
3.1.1
Residuals
. 48
3.1.2
Using Plots of Residuals to Determine Whether
the Proposed Regression Model Is a Valid Model
. 49
3.1.3
Example of a Quadratic Model
. 50
3.2
Regression Diagnostics: Tools for Checking
the Validity of a Model
. 50
3.2.1
Leverage Points
. 51
3.2.2
Standardized Residuals
. 59
3.2.3
Recommendations for Handling Outliers
and Leverage Points
. 66
3.2.4
Assessing the Influence of Certain Cases
. 67
3.2.5
Normality of the Errors
. 69
3.2.6
Constant Variance
. 71
3.3
Transformations
. 76
3.3.1
Using Transformations to Stabilize Variance
. 76
3.3.2
Using Logarithms to Estimate Percentage Effects
. 79
3.3.3
Using Transformations to Overcome Problems
due to Nonlinearity
. 83
3.4
Exercises
. 103
4
Weighted Least Squares
. 115
4.1
Straight-Line Regression Based on Weighted Least Squares
. 115
4.1.1
Prediction Intervals for Weighted Least Squares
. 118
4.1.2
Leverage for Weighted Least Squares
. 118
4.1.3
Using Least Squares to Calculate Weighted Least Squares.
119
4.1.4
Defining Residuals for Weighted Least Squares
. 121
4.1.5
The Use of Weighted Least Squares
. 121
4.2
Exercises
. 122
5
Multiple Linear Regression
. 125
5.1
Polynomial Regression
. 125
5.2
Estimation and Inference in Multiple Linear Regression
. 130
5.3
Analysis of Covariance
. 140
5.4
Exercises
. 146
6
Diagnostics and Transformations for Multiple Linear Regression
. 151
6.1
Regression Diagnostics for Multiple Regression
. 151
6.1.1
Leverage Points in Multiple Regression
. 152
6.1.2
Properties of Residuals in Multiple Regression
. 154
6.1.3
Added Variable Plots
. 162
Contents xiii
6.2
Transformations
. 167
6.2.1
Using Transformations to Overcome Nonlinearity
. 167
6.2.2
Using Logarithms to Estimate Percentage Effects:
Real Valued Predictor Variables
. 184
6.3
Graphical Assessment of the Mean Function Using
Marginal Model Plots
. 189
6.4
Multicollinearity
. 195
6.4.1
Multicollinearity and Variance Inflation Factors
. 203
6.5
Case Study: Effect of Wine Critics' Ratings on Prices
of Bordeaux Wines
. 203
6.6
Pitfalls of Observational Studies Due to Omitted Variables
. 210
6.6.1
Spurious Correlation
Dueto
Omitted Variables
. 210
6.6.2
The Mathematics of Omitted Variables
. 213
6.6.3
Omitted Variables in Observational Studies
. 214
6.7
Exercises
. 215
7
Variable Selection
. 227
7.1
Evaluating Potential Subsets of Predictor Variables
. 228
7.1.1
Criterion
1 :
R2-Adjusted
. 228
7.1.2
Criterion
2:
AIC, Akaike's Information Criterion
. 230
7.1.3
Criterion
3:
AICC,
Corrected AIC
. 231
7.1.4
Criterion
4:
BIC,
Bayesian Information Criterion
. 232
7.1.5
Comparison of AIC, AICC and
BIC
. 232
7.2
Deciding on the Collection of Potential Subsets
of Predictor Variables
. 233
7.2.1
All Possible Subsets
. 233
7.2.2
Stepwise Subsets
. 236
7.2.3
Inference After Variable Selection
. 238
7.3
Assessing the Predictive Ability of Regression Models
. 239
7.3.1
Stage
1 :
Model Building Using the Training Data Set
. 239
7.3.2
Stage
2:
Model Comparison Using the Test Data Set
. 247
7.4
Recent Developments in Variable Selection
-
LASSO
. 250
7.5
Exercises
. 252
8
Logistic Regression
. 263
8.1
Logistic Regression Based on a Single Predictor
. 263
8.1.1
The Logistic Function and Odds
. 265
8.1.2
Likelihood for Logistic Regression with
a Single Predictor
. 268
8.1.3
Explanation of Deviance
. 271
8.1.4
Using Differences in Deviance Values
to Compare Models
. 272
8.1.5
R: for Logistic Regression
. 273
8.1.6
Residuals for Logistic Regression
. 274
xiv
Contents
8.2
Binary Logistic Regression
. 277
8.2.1
Deviance for the Case of Binary Data
. 280
8.2.2
Residuals for Binary Data
. 281
8.2.3
Transforming Predictors in Logistic Regression
for Binary Data
. 282
8.2.4
Marginal Model Plots for Binary Data
. 286
8.3
Exercises
. 294
9
Serially Correlated Errors
. 305
9.1
Autocorrelation
. 305
9.2
Using Generalized Least Squares When the Errors Are AR(1)
. 310
9.2.1
Generalized Least Squares Estimation
. 311
9.2.2
Transforming a Model with AR(
1 )
Errors into
a Model with iid Errors
. 315
9.2.3
A General Approach to Transforming GLS into LS
. 316
9.3
Case Study
. 319
9.4
Exercises
. 325
10
Mixed Models
. 331
10.1
Random Effects
. 331
10.1.1
Maximum Likelihood and Restricted
Maximum Likelihood
. 334
10.1.2
Residuals in Mixed Models
. 345
10.2
Models with Covariance Structures Which Vary Over Time
. 353
10.2.1
Modeling the Conditional Mean
. 354
10.3
Exercises
. 368
Appendix: Nonparametric Smoothing
. 371
References
. 383
Index
. 387 |
| adam_txt |
Contents
1
Introduction
. 1
1.1 Building
Valid
Models. 1
1.2
Motivating Examples
. 1
1.2.1
Assessing the Ability of NFL Kickers
. 1
1.2.2
Newspaper Circulation
. 4
1.2.3
Menu Pricing in a New Italian Restaurant
in New York City
. 5
1.2.4
Effect of Wine Critics' Ratings on Prices
of Bordeaux Wines
. 8
1.3
Level of Mathematics
. 13
2
Simple Linear Regression
. 15
2.1
Introduction and Least Squares Estimates
. 15
2.1.1
Simple Linear Regression Models
. 15
2.2
Inferences About the Slope and the Intercept
. 20
2.2.1
Assumptions Necessary in Order to Make Inferences
About the Regression Model
. 21
2.2.2
Inferences About the Slope of the Regression Line
. 21
2.2.3
Inferences About the Intercept of the Regression Line
. 23
2.3
Confidence Intervals for the Population Regression Line
. 24
2.4
Prediction Intervals for the Actual Value of
Y
. 25
2.5
Analysis of Variance
. 27
2.6
Dummy Variable Regression
. 30
2.7
Derivations of Results
. 33
2.7.1
Inferences about the Slope of the Regression Line
. 34
2.7.2
Inferences about the Intercept of the Regression Line
. 35
2.7.3
Confidence Intervals for the Population Regression Line
. 36
2.7.4
Prediction Intervals for the Actual Value of
Y
. 37
2.8
Exercises
. 38
xii Contents
3
Diagnostics and Transformations for Simple
Linear Regression
. 45
3.1
Valid and Invalid Regression Models:
Anscombe's Four Data Sets
. 45
3.1.1
Residuals
. 48
3.1.2
Using Plots of Residuals to Determine Whether
the Proposed Regression Model Is a Valid Model
. 49
3.1.3
Example of a Quadratic Model
. 50
3.2
Regression Diagnostics: Tools for Checking
the Validity of a Model
. 50
3.2.1
Leverage Points
. 51
3.2.2
Standardized Residuals
. 59
3.2.3
Recommendations for Handling Outliers
and Leverage Points
. 66
3.2.4
Assessing the Influence of Certain Cases
. 67
3.2.5
Normality of the Errors
. 69
3.2.6
Constant Variance
. 71
3.3
Transformations
. 76
3.3.1
Using Transformations to Stabilize Variance
. 76
3.3.2
Using Logarithms to Estimate Percentage Effects
. 79
3.3.3
Using Transformations to Overcome Problems
due to Nonlinearity
. 83
3.4
Exercises
. 103
4
Weighted Least Squares
. 115
4.1
Straight-Line Regression Based on Weighted Least Squares
. 115
4.1.1
Prediction Intervals for Weighted Least Squares
. 118
4.1.2
Leverage for Weighted Least Squares
. 118
4.1.3
Using Least Squares to Calculate Weighted Least Squares.
119
4.1.4
Defining Residuals for Weighted Least Squares
. 121
4.1.5
The Use of Weighted Least Squares
. 121
4.2
Exercises
. 122
5
Multiple Linear Regression
. 125
5.1
Polynomial Regression
. 125
5.2
Estimation and Inference in Multiple Linear Regression
. 130
5.3
Analysis of Covariance
. 140
5.4
Exercises
. 146
6
Diagnostics and Transformations for Multiple Linear Regression
. 151
6.1
Regression Diagnostics for Multiple Regression
. 151
6.1.1
Leverage Points in Multiple Regression
. 152
6.1.2
Properties of Residuals in Multiple Regression
. 154
6.1.3
Added Variable Plots
. 162
Contents xiii
6.2
Transformations
. 167
6.2.1
Using Transformations to Overcome Nonlinearity
. 167
6.2.2
Using Logarithms to Estimate Percentage Effects:
Real Valued Predictor Variables
. 184
6.3
Graphical Assessment of the Mean Function Using
Marginal Model Plots
. 189
6.4
Multicollinearity
. 195
6.4.1
Multicollinearity and Variance Inflation Factors
. 203
6.5
Case Study: Effect of Wine Critics' Ratings on Prices
of Bordeaux Wines
. 203
6.6
Pitfalls of Observational Studies Due to Omitted Variables
. 210
6.6.1
Spurious Correlation
Dueto
Omitted Variables
. 210
6.6.2
The Mathematics of Omitted Variables
. 213
6.6.3
Omitted Variables in Observational Studies
. 214
6.7
Exercises
. 215
7
Variable Selection
. 227
7.1
Evaluating Potential Subsets of Predictor Variables
. 228
7.1.1
Criterion
1 :
R2-Adjusted
. 228
7.1.2
Criterion
2:
AIC, Akaike's Information Criterion
. 230
7.1.3
Criterion
3:
AICC,
Corrected AIC
. 231
7.1.4
Criterion
4:
BIC,
Bayesian Information Criterion
. 232
7.1.5
Comparison of AIC, AICC and
BIC
. 232
7.2
Deciding on the Collection of Potential Subsets
of Predictor Variables
. 233
7.2.1
All Possible Subsets
. 233
7.2.2
Stepwise Subsets
. 236
7.2.3
Inference After Variable Selection
. 238
7.3
Assessing the Predictive Ability of Regression Models
. 239
7.3.1
Stage
1 :
Model Building Using the Training Data Set
. 239
7.3.2
Stage
2:
Model Comparison Using the Test Data Set
. 247
7.4
Recent Developments in Variable Selection
-
LASSO
. 250
7.5
Exercises
. 252
8
Logistic Regression
. 263
8.1
Logistic Regression Based on a Single Predictor
. 263
8.1.1
The Logistic Function and Odds
. 265
8.1.2
Likelihood for Logistic Regression with
a Single Predictor
. 268
8.1.3
Explanation of Deviance
. 271
8.1.4
Using Differences in Deviance Values
to Compare Models
. 272
8.1.5
R: for Logistic Regression
. 273
8.1.6
Residuals for Logistic Regression
. 274
xiv
Contents
8.2
Binary Logistic Regression
. 277
8.2.1
Deviance for the Case of Binary Data
. 280
8.2.2
Residuals for Binary Data
. 281
8.2.3
Transforming Predictors in Logistic Regression
for Binary Data
. 282
8.2.4
Marginal Model Plots for Binary Data
. 286
8.3
Exercises
. 294
9
Serially Correlated Errors
. 305
9.1
Autocorrelation
. 305
9.2
Using Generalized Least Squares When the Errors Are AR(1)
. 310
9.2.1
Generalized Least Squares Estimation
. 311
9.2.2
Transforming a Model with AR(
1 )
Errors into
a Model with iid Errors
. 315
9.2.3
A General Approach to Transforming GLS into LS
. 316
9.3
Case Study
. 319
9.4
Exercises
. 325
10
Mixed Models
. 331
10.1
Random Effects
. 331
10.1.1
Maximum Likelihood and Restricted
Maximum Likelihood
. 334
10.1.2
Residuals in Mixed Models
. 345
10.2
Models with Covariance Structures Which Vary Over Time
. 353
10.2.1
Modeling the Conditional Mean
. 354
10.3
Exercises
. 368
Appendix: Nonparametric Smoothing
. 371
References
. 383
Index
. 387 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Sheather, Simon J. |
| author_facet | Sheather, Simon J. |
| author_role | aut |
| author_sort | Sheather, Simon J. |
| author_variant | s j s sj sjs |
| building | Verbundindex |
| bvnumber | BV035153783 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | DAT 307f MAT 628f |
| ctrlnum | (OCoLC)611231596 (DE-599)DNB98974020X |
| dewey-full | 519.536 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.536 |
| dewey-search | 519.536 |
| dewey-sort | 3519.536 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Informatik Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV035153783 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:47:47Z |
| indexdate | 2024-09-10T00:56:07Z |
| institution | BVB |
| isbn | 9780387096070 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016960994 |
| oclc_num | 611231596 |
| open_access_boolean | |
| owner | DE-945 DE-824 DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-11 DE-384 DE-188 DE-83 |
| owner_facet | DE-945 DE-824 DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-11 DE-384 DE-188 DE-83 |
| physical | XIV, 392 Seiten Illustrationen |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spelling | Sheather, Simon J. Verfasser aut A modern approach to regression with R Simon J. Sheather New York, NY Springer [2009] © 2009 XIV, 392 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Analyse de régression R (Langage de programmation) R (computerprogramma) gtt Regressieanalyse gtt R (Computer program language) Regression analysis R Programm (DE-588)4705956-4 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 s R Programm (DE-588)4705956-4 s b DE-604 Erscheint auch als Online-Ausgabe 978-0-387-09608-7 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016960994&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sheather, Simon J. A modern approach to regression with R Analyse de régression R (Langage de programmation) R (computerprogramma) gtt Regressieanalyse gtt R (Computer program language) Regression analysis R Programm (DE-588)4705956-4 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4127980-3 |
| title | A modern approach to regression with R |
| title_auth | A modern approach to regression with R |
| title_exact_search | A modern approach to regression with R |
| title_exact_search_txtP | A modern approach to regression with R |
| title_full | A modern approach to regression with R Simon J. Sheather |
| title_fullStr | A modern approach to regression with R Simon J. Sheather |
| title_full_unstemmed | A modern approach to regression with R Simon J. Sheather |
| title_short | A modern approach to regression with R |
| title_sort | a modern approach to regression with r |
| topic | Analyse de régression R (Langage de programmation) R (computerprogramma) gtt Regressieanalyse gtt R (Computer program language) Regression analysis R Programm (DE-588)4705956-4 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| topic_facet | Analyse de régression R (Langage de programmation) R (computerprogramma) Regressieanalyse R (Computer program language) Regression analysis R Programm Regressionsmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016960994&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sheathersimonj amodernapproachtoregressionwithr |