A Modern Approach to Regression With R

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ISBN: 9780387096070 | 0387096078
Cover: Hardcover
Copyright: 9/30/2009

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A Modern Approach to Regression with R focuses on tools and techniques for building regression models using real-world data and assessing their validity. When a weakness in the model is identified, the next step is to address this weakness. A key theme throughout the book is that it makes sense to base inferences or conclusions only on valid models.

Introduction	p. 1
Building Valid Models	p. 1
Motivating Examples	p. 1
Assessing the Ability of NFL Kickers	p. 1
Newspaper Circulation	p. 1
Menu Pricing in a New Italian Restaurant in New York City	p. 5
Effect of Wine Critics' Ratings on Prices of Bordeaux Wines	p. 8
Level of Mathematics	p. 13
Simple Linear Regression	p. 15
Introduction and Least Squares Estimates	p. 15
Simple Linear Regression Models	p. 15
Inferences About the Slope and the Intercept	p. 20
Assumptions Necessary in Order to Make Inferences About the Regression Model	p. 21
Inferences About the Slope of the Regression Line	p. 21
Inferences About the Intercept of the Regression Line	p. 23
Confidence Intervals for the Population Regression Line	p. 24
Prediction Intervals for the Actual Value of Y	p. 25
Analysis of Variance	p. 27
Dummy Variable Regression	p. 30
Derivations of Results	p. 33
Inferences about the Slope of the Regression Line	p. 34
Inferences about the Intercept of the Regression Line	p. 35
Confidence Intervals for the Population Regression Line	p. 36
Prediction Intervals for the Actual Value of Y	p. 37
Exercises	p. 38
Diagnostics and Transformations for Simple Linear Regression	p. 45
Valid and Invalid Regression Models: Anscombe's Four Data Sets	p. 45
Residuals	p. 48
Using Plots of Residuals to Determine Whether the Proposed Regression Model Is a Valid Model	p. 49
Example of a Quadratic Model	p. 50
Regression Diagnostics: Tools for Checking the Validity of a Model	p. 50
Leverage Points	p. 51
Standardized Residuals	p. 59
Recommendations for Handling Outliers and Leverage Points	p. 66
Assessing the Influence of Certain Cases	p. 67
Normality of the Errors	p. 69
Constant Variance	p. 71
Transformations	p. 76
Using Transformations to Stabilize Variance	p. 76
Using Logarithms to Estimate Percentage Effects	p. 79
Using Transformations to Overcome Problems due to Nonlinearity	p. 83
Exercises	p. 103
Weighted Least Squares	p. 115
Straight-Line Regression Based on Weighted Least Squares	p. 115
Prediction Intervals for Weighted Least Squares	p. 118
Leverage for Weighted Least Squares	p. 118
Using Least Squares to Calculate Weighted Least Squares	p. 119
Defining Residuals for Weighted Least Squares	p. 121
The Use of Weighted Least Squares	p. 121
Exercises	p. 122
Multiple Linear Regression	p. 125
Polynomial Regression	p. 125
Estimation and Inference in Multiple Linear Regression	p. 130
Analysis of Covariance	p. 140
Exercises	p. 146
Diagnostics and Transformations for Multiple Linear Regression	p. 151
Regression Diagnostics for Multiple Regression	p. 151
Leverage Points in Multiple Regression	p. 152
Properties of Residuals in Multiple Regression	p. 154
Added Variable Plots	p. 162
Transformations	p. 167
Using Transformations to Overcome Nonlinearity	p. 167
Using Logarithms to Estimate Percentage Effects: Real Valued Predictor Variables	p. 184
Graphical Assessment of the Mean Function Using Marginal Model Plots	p. 189
Multicollinearity	p. 195
Multicollinearity and Variance Inflation Factors	p. 203
Case Study: Effect of Wine Critics' Ratings on Prices of Bordeaux Wines	p. 203
Pitfalls of Observational Studies Due to Omitted Variables	p. 210
Spurious Correlation Due to Omitted Variables	p. 210
The Mathematics of Omitted Variables	p. 213
Omitted Variables in Observational Studies	p. 214
Exercises	p. 215
Variable Selection	p. 227
Evaluating Potential Subsets of Predictor Variables	p. 228
Criterion 1: R2-Adjusted	p. 228
Criterion 2: AICc, Akaike's Information Criterion	p. 230
Criterion 3: AICc, Corrected AIC	p. 231
Criterion 4: BIC, Bayesian Information Criterion	p. 232
Comparison of AIC, AICc and BIC	p. 232
Deciding on the Collection of Potential Subsets of Predictor Variables	p. 233
All Possible Subsets	p. 233
Stepwise Subsets	p. 236
Inference After Variable Selection	p. 238
Assessing the Predictive Ability of Regression Models	p. 239
Stage 1: Model Building Using the Training Data Set	p. 239
Stage 2: Model Comparison Using the Test Data Set	p. 247
Recent Developments in Variable Selection-LASSO	p. 250
Exercises	p. 252
Logistic Regression	p. 263
Logistic Regression Based on a Single Predictor	p. 263
The Logistic Function and Odds	p. 265
Likelihood for Logistic Regression with a Single Predictor	p. 268
Explanation of Deviance	p. 271
Using Differences in Deviance Values to Compare Models	p. 272
R2 for Logistic Regression	p. 273
Residuals for Logistic Regression	p. 274
Binary Logistic Regression	p. 277
Deviance for the Case of Binary Data	p. 280
Residuals for Binary Data	p. 281
Transforming Predictors in Logistic Regression for Binary Data	p. 282
Marginal Model Plots for Binary Data	p. 286
Exercises	p. 294
Serially Correlated Errors	p. 305
Autocorrelation	p. 305
Using Generalized Least Squares When the Errors Are AR(1)	p. 310
Generalized Least Squares Estimation	p. 311
Transforming a Model with AR(1) Errors into a Model with iid Errors	p. 315
A General Approach to Transforming GLS into LS	p. 316
Case Study	p. 319
Exercises	p. 325
Mixed Models	p. 331
Random Effects	p. 331
Maximum Likelihood and Restricted Maximum Likelihood	p. 334
Residuals in Mixed Models	p. 345
Models with Covariance Structures Which Vary Over Time	p. 353
Modeling the Conditional Mean	p. 354
Exercises	p. 368
Appendix: Nonparametric Smoothing	p. 371
References	p. 383
Index	p. 387
Table of Contents provided by Ingram. All Rights Reserved.

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A Modern Approach to Regression With R

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