Modern Approach to Regression with R

ISBN-10: 0387096078
ISBN-13: 9780387096070
Edition: 2009
List price: $62.99 Buy it from $38.86 Rent it from $20.05
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Description: Focusing on the tools and techniques used for building valid regression models using real-world data, this text stresses the need to base inferences or conclusions on valid models.

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Book details

List price: $62.99
Copyright year: 2009
Publisher: Springer London, Limited
Publication date: 3/11/2009
Binding: Hardcover
Pages: 393
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.848
Language: English

Focusing on the tools and techniques used for building valid regression models using real-world data, this text stresses the need to base inferences or conclusions on valid models.

Introduction
Building Valid Models
Motivating Examples
Assessing the Ability of NFL Kickers
Newspaper Circulation
Menu Pricing in a New Italian Restaurant in New York City
Effect of Wine Critics' Ratings on Prices of Bordeaux Wines
Level of Mathematics
Simple Linear Regression
Introduction and Least Squares Estimates
Simple Linear Regression Models
Inferences About the Slope and the Intercept
Assumptions Necessary in Order to Make Inferences About the Regression Model
Inferences About the Slope of the Regression Line
Inferences About the Intercept of the Regression Line
Confidence Intervals for the Population Regression Line
Prediction Intervals for the Actual Value of Y
Analysis of Variance
Dummy Variable Regression
Derivations of Results
Inferences about the Slope of the Regression Line
Inferences about the Intercept of the Regression Line
Confidence Intervals for the Population Regression Line
Prediction Intervals for the Actual Value of Y
Exercises
Diagnostics and Transformations for Simple Linear Regression
Valid and Invalid Regression Models: Anscombe's Four Data Sets
Residuals
Using Plots of Residuals to Determine Whether the Proposed Regression Model Is a Valid Model
Example of a Quadratic Model
Regression Diagnostics: Tools for Checking the Validity of a Model
Leverage Points
Standardized Residuals
Recommendations for Handling Outliers and Leverage Points
Assessing the Influence of Certain Cases
Normality of the Errors
Constant Variance
Transformations
Using Transformations to Stabilize Variance
Using Logarithms to Estimate Percentage Effects
Using Transformations to Overcome Problems due to Nonlinearity
Exercises
Weighted Least Squares
Straight-Line Regression Based on Weighted Least Squares
Prediction Intervals for Weighted Least Squares
Leverage for Weighted Least Squares
Using Least Squares to Calculate Weighted Least Squares
Defining Residuals for Weighted Least Squares
The Use of Weighted Least Squares
Exercises
Multiple Linear Regression
Polynomial Regression
Estimation and Inference in Multiple Linear Regression
Analysis of Covariance
Exercises
Diagnostics and Transformations for Multiple Linear Regression
Regression Diagnostics for Multiple Regression
Leverage Points in Multiple Regression
Properties of Residuals in Multiple Regression
Added Variable Plots
Transformations
Using Transformations to Overcome Nonlinearity
Using Logarithms to Estimate Percentage Effects: Real Valued Predictor Variables
Graphical Assessment of the Mean Function Using Marginal Model Plots
Multicollinearity
Multicollinearity and Variance Inflation Factors
Case Study: Effect of Wine Critics' Ratings on Prices of Bordeaux Wines
Pitfalls of Observational Studies Due to Omitted Variables
Spurious Correlation Due to Omitted Variables
The Mathematics of Omitted Variables
Omitted Variables in Observational Studies
Exercises
Variable Selection
Evaluating Potential Subsets of Predictor Variables
Criterion 1: R2-Adjusted
Criterion 2: AICc, Akaike's Information Criterion
Criterion 3: AICc, Corrected AIC
Criterion 4: BIC, Bayesian Information Criterion
Comparison of AIC, AICc and BIC
Deciding on the Collection of Potential Subsets of Predictor Variables
All Possible Subsets
Stepwise Subsets
Inference After Variable Selection
Assessing the Predictive Ability of Regression Models
Stage 1: Model Building Using the Training Data Set
Stage 2: Model Comparison Using the Test Data Set
Recent Developments in Variable Selection-LASSO
Exercises
Logistic Regression
Logistic Regression Based on a Single Predictor
The Logistic Function and Odds
Likelihood for Logistic Regression with a Single Predictor
Explanation of Deviance
Using Differences in Deviance Values to Compare Models
R2 for Logistic Regression
Residuals for Logistic Regression
Binary Logistic Regression
Deviance for the Case of Binary Data
Residuals for Binary Data
Transforming Predictors in Logistic Regression for Binary Data
Marginal Model Plots for Binary Data
Exercises
Serially Correlated Errors
Autocorrelation
Using Generalized Least Squares When the Errors Are AR(1)
Generalized Least Squares Estimation
Transforming a Model with AR(1) Errors into a Model with iid Errors
A General Approach to Transforming GLS into LS
Case Study
Exercises
Mixed Models
Random Effects
Maximum Likelihood and Restricted Maximum Likelihood
Residuals in Mixed Models
Models with Covariance Structures Which Vary Over Time
Modeling the Conditional Mean
Exercises
Appendix: Nonparametric Smoothing
References
Index

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