Linear regression analysis: theory and computing
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 317 - 324 |
| Physical Description: | XIX, 328 S. graph. Darst. |
| ISBN: | 9789812834102 9812834109 |
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MARC
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| 100 | 1 | |a Yan, Xin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear regression analysis |b theory and computing |c Xin Yan ; Xiao Gang Su |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2009 | |
| 300 | |a XIX, 328 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 317 - 324 | ||
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Record in the Search Index
| _version_ | 1804138609166516224 |
|---|---|
| adam_text | Contents
Preface
v
List of Figures
xv
List of Tables
xvii
1.
Introduction
1
1.1
Regression Model
....................... 1
1.2
Goals of Regression Analysis
................ 4
1.3
Statistical Computing in Regression Analysis
....... 5
2.
Simple Linear Regression
9
2.1
Introduction
.......................... 9
2.2
Least Squares Estimation
.................. 10
2.3
Statistical Properties of the Least Squares Estimation
. . 13
2.4
Maximum Likelihood Estimation
.............. 18
2.5
Confidence Interval on Regression Mean and Regression
Prediction
........................... 19
2.6
Statistical Inference on Regression Parameters
...... 21
2.7
Residual Analysis and Model Diagnosis
.......... 25
2.8
Example
............................ 28
3.
Multiple Linear Regression
41
3.1
Vector Space and Projection
................. 41
3.1.1
Vector Space
..................... 41
3.1.2
Linearly Independent Vectors
........... 44
3.1.3
Dot Product and Projection
............ 44
Linear
Regression
Analysis: Theory and Computing
3.2
Matrix Form of Multiple Linear Regression
........ 48
3.3
Quadratic Form of Random Variables
........... 49
3.4
Idempotent Matrices
..................... 50
3.5
Multivariate Normal Distribution
.............. 54
3.6
Quadratic Form of the Multivariate Normal Variables
. . 56
3.7
Least Squares Estimates of the Multiple Regression
Parameters
.......................... 58
3.8
Matrix Form of the Simple Linear Regression
....... 62
3.9
Test for Full Model and Reduced Model
.......... 64
3.10
Test for General Linear Hypothesis
............. 66
3.11
The Least Squares Estimates of Multiple Regression
Parameters Under Linear Restrictions
........... 67
3.12
Confidence Intervals of Mean and Prediction in Multiple
Regression
........................... 69
3.13
Simultaneous Test for Regression Parameters
....... 70
3.14
Bonferroni Confidence Region for Regression Parameters
. 71
3.15
Interaction and Confounding
................ 72
3.15.1
Interaction
...................... 73
3.15.2
Confounding
..................... 75
3.16
Regression with Dummy Variables
............. 77
3.17
Collinearity in Multiple Linear Regression
......... 81
3.17.1
Collinearity
...................... 81
3.17.2
Variance Inflation
.................. 85
3.18
Linear Model in Centered Form
............... 87
3.19
Numerical Computation of
LSE
via QR Decomposition
. 92
3.19.1
Orthogonalization
.................. 92
3.19.2
QR Decomposition and
LSE
............ 94
3.20
Analysis of Regression Residual
............... 96
3.20.1
Purpose of the Residual Analysis
......... 96
3.20.2
Residual Plot
.................... 97
3.20.3
Studentized Residuals
................ 103
3.20.4
PRESS Residual
................... 103
3.20.5
Identify Outlier Using PRESS Residual
...... 106
3.20.6
Test for Mean Shift Outlier
............. 108
3.21
Check for Normality of the Error Term in Multiple
Regression
........................... 115
3.22
Example
............................
П5
Contents xi
4.
Detection of Outliers and Influential Observations
in Multiple Linear Regression
129
4.1
Model Diagnosis for Multiple Linear Regression
...... 130
4.1.1
Simple Criteria for Model Comparison
...... 130
4.1.2
Bias in Error Estimate from Under-specified Model
131
4.1.3
Cross Validation
................... 132
4.2
Detection of Outliers in Multiple Linear Regression
.... 133
4.3
Detection of Influential Observations in Multiple Linear
Regression
........................... 134
4.3.1
Influential Observation
............... 134
4.3.2
Notes on Outlier and Influential Observation
. . . 136
4.3.3
Residual Mean Square Error for Over-fitted
Regression Model
.................. 137
4.4
Test for Mean-shift Outliers
................. 139
4.5
Graphical Display of Regression Diagnosis
......... 142
4.5.1
Partial Residual Plot
................ 142
4.5.2
Component-plus-residual Plot
........... 146
4.5.3
Augmented Partial Residual Plot
......... 147
4.6
Test for Inferential Observations
.............. 147
4.7
Example
............................ 150
5.
Model Selection
157
5.1
Effect of Underfitting and Overfitting
........... 157
5.2
All Possible Regressions
................... 165
5.2.1
Some Naive Criteria
................ 165
5.2.2
PRESS and GCV
.................. 166
5.2.3
Mallow s CP
..................... 167
5.2.4
AIC, AICc, and
BIC
................ 169
5.3
Stepwise Selection
...................... 171
5.3.1
Backward Elimination
................ 171
5.3.2
Forward Addition
.................. 172
5.3.3
Stepwise Search
................... 172
5.4
Examples
........................... 173
5.5
Other Related Issues
.................... 179
5.5.1
Variance Importance or Relevance
........ 180
5.5.2
PCA and SIR
.................... 186
xii
Linear Regression Analysis: Theory and Computing
6.
Model Diagnostics
195
6.1
Test Heteroscedasticity
.................... 197
6.1.1
Heteroscedasticity
.................. 197
6.1.2
Likelihood Ratio Test,
Wald,
and
Lagrange
Multi¬
plier Test
....................... 198
6.1.3
Tests for Heteroscedasticity
............. 201
6.2
Detection of Regression Functional Form
.......... 204
6.2.1
Box
-Сох
Power Transformation
.......... 205
6.2.2
Additive Models
................... 207
6.2.3
ACE and
AVAS
................... 210
6.2.4
Example
....................... 211
7.
Extensions of Least Squares
219
7.1
Non-
Full-Rank Linear Regression Models
......... 219
7.1.1
Generalized Inverse
................. 221
7.1.2
Statistical Inference on Null-Full-Rank Regression
Models
........................ 223
7.2
Generalized Least Squares
.................. 229
7.2.1
Estimation of
(β, σ2) ................
230
7.2.2
Statistical Inference
................. 231
7.2.3
Misspecification of the Error Variance Structure
. 232
7.2.4
Typical Error Variance Structures
........ 233
7.2.5
Example
....................... 236
7.3
Ridge Regression and LASSO
................ 238
7.3.1
Ridge Shrinkage Estimator
............. 239
7.3.2
Connection with PCA
............... 243
7.3.3
LASSO and Other Extensions
........... 246
7.3.4
Example
....................... 250
7.4
Parametric Nonlinear Regression
.............. 259
7.4.1
Least Squares Estimation in Nonlinear Regression
261
7.4.2
Example
....................... 263
8.
Generalized Linear Models
269
8.1
Introduction: A Motivating Example
............ 269
8.2
Components of GLM
.................... 272
8.2.1
Exponential Family
................. 272
8.2.2
Linear Predictor and Link Functions
....... 273
8.3
Maximum Likelihood Estimation of GLM
......... 274
Contents xiii
8.3.1
Likelihood Equations
................ 274
8.3.2
Fisher s Information Matrix
............ 275
8.3.3
Optimization of the Likelihood
........... 276
8.4
Statistical Inference and Other Issues in GLM
...... 278
8.4.1 Wald,
Likelihood Ratio, and Score Test
..... 278
8.4.2
Other Model Fitting Issues
............ 281
8.5
Logistic Regression for Binary Data
............ 282
8.5.1
Interpreting the Logistic Model
.......... 282
8.5.2
Estimation of the Logistic Model
......... 284
8.5.3
Example
....................... 285
8.6
Poisson
Regression for Count Data
............ 287
8.6.1
The
Loglinear
Model
................ 287
8.6.2
Example
....................... 288
9.
Bayesian Linear Regression
297
9.1
Bayesian Linear Models
................... 297
9.1.1
Bayesian Inference in General
........... 297
9.1.2
Conjugate Normal-Gamma Priors
......... 299
9.1.3
Inference in Bayesian Linear Model
........ 302
9.1.4
Bayesian Inference via MCMC
........... 303
9.1.5
Prediction
...................... 306
9.1.6
Example
....................... 307
9.2
Bayesian Model Averaging
................. 309
Bibliography
317
Index
325
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T21:30:54Z |
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| isbn | 9789812834102 9812834109 |
| language | English |
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| spelling | Yan, Xin Verfasser aut Linear regression analysis theory and computing Xin Yan ; Xiao Gang Su Singapore [u.a.] World Scientific 2009 XIX, 328 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 317 - 324 Regression stw Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Lineare Regression (DE-588)4167709-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineare Regression (DE-588)4167709-2 s Regressionsanalyse (DE-588)4129903-6 s DE-604 Su, Xiao Gang Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017111386&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yan, Xin Su, Xiao Gang Linear regression analysis theory and computing Regression stw Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Lineare Regression (DE-588)4167709-2 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4167709-2 (DE-588)4123623-3 |
| title | Linear regression analysis theory and computing |
| title_auth | Linear regression analysis theory and computing |
| title_exact_search | Linear regression analysis theory and computing |
| title_full | Linear regression analysis theory and computing Xin Yan ; Xiao Gang Su |
| title_fullStr | Linear regression analysis theory and computing Xin Yan ; Xiao Gang Su |
| title_full_unstemmed | Linear regression analysis theory and computing Xin Yan ; Xiao Gang Su |
| title_short | Linear regression analysis |
| title_sort | linear regression analysis theory and computing |
| title_sub | theory and computing |
| topic | Regression stw Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Lineare Regression (DE-588)4167709-2 gnd |
| topic_facet | Regression Regression analysis Regressionsanalyse Lineare Regression Lehrbuch |
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