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Linear Models with R

Julian J. Faraway
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2014
Number of Pages: 
274
Format: 
Hardcover
Edition: 
2
Series: 
Texts in Statistical Science
Price: 
89.95
ISBN: 
9781439887332
Category: 
Textbook
[Reviewed by
Priya Kohli
, on
01/6/2015
]

As the title implies, the book is a text on the core topic of linear models with a slant toward applications. The data examples cover a broad range of fields including physical sciences, engineering, social sciences, and economics. The book provides an excellent introduction of the various aspects of linear models with many interesting examples.

The explanations are clear enough for beginners with little statistical background and are accompanied by worked examples with associated R code. This is an important contribution, since it provides the readers/students an opportunity to replicate the analyses and results of an example. There are many books written on the topic of linear models, but this book takes an applied approach and explains the concepts intuitively, using graphical explanations and examples.

Overall this is a nicely written book, which can lay a strong foundation for senior undergraduate and beginning graduate students. This book can be recommended as a textbook for computational linear regression courses. It will also be useful for practitioners who want to get started on applying regression models for studying associations among different variables, estimation of regression coefficients, and prediction. It offers insightful interpretations and discussions with examples worked using the R software. 


Priya Kohli is an Assistant Professor of Statistics at the Connecticut College. She holds a Master’s degree in Applied Probability and Statistics from Northern Illinois University and a PhD in Statistics from Texas A&M University. Her current research interests include covariance modeling, high-dimensional data modeling, time series analysis, spatial statistics, and multivariate data modeling.

Introduction
Before You Start
Initial Data Analysis
When to Use Linear Modeling
History

Estimation
Linear Model
Matrix Representation
Estimating b
Least Squares Estimation
Examples of Calculating ˆb
Example
QR Decomposition
Gauss–Markov Theorem
Goodness of Fit
Identifiability
Orthogonality

Inference
Hypothesis Tests to Compare Models
Testing Examples
Permutation Tests
Sampling
Confidence Intervals for b
Bootstrap Confidence Intervals

Prediction
Confidence Intervals for Predictions
Predicting Body Fat
Autoregression
What Can Go Wrong with Predictions?

Explanation
Simple Meaning
Causality
Designed Experiments
Observational Data
Matching
Covariate Adjustment
Qualitative Support for Causation

Diagnostics
Checking Error Assumptions
Finding Unusual Observations 
Checking the Structure of the Model
Discussion

Problems with the Predictors
Errors in the Predictors
Changes of Scale
Collinearity

Problems with the Error
Generalized Least Squares
Weighted Least Squares
Testing for Lack of Fit
Robust Regression

Transformation
Transforming the Response
Transforming the Predictors
Broken Stick Regression
Polynomials
Splines
Additive Models
More Complex Models

Model Selection
Hierarchical Models
Testing-Based Procedures
Criterion-Based Procedures
Summary

Shrinkage Methods
Principal Components
Partial Least Squares
Ridge Regression
Lasso

Insurance Redlining—A Complete Example
Ecological Correlation
Initial Data Analysis
Full Model and Diagnostics
Sensitivity Analysis
Discussion

Missing Data
Types of Missing Data
Deletion
Single Imputation
Multiple Imputation

Categorical Predictors
A Two-Level Factor
Factors and Quantitative Predictors
Interpretation with Interaction Terms
Factors with More than Two Levels
Alternative Codings of Qualitative Predictors

One Factor Models
The Model
An Example
Diagnostics
Pairwise Comparisons
False Discovery Rate

Models with Several Factors
Two Factors with No Replication
Two Factors with Replication
Two Factors with an Interaction
Larger Factorial Experiments

Experiments with Blocks
Randomized Block Design
Latin Squares
Balanced Incomplete Block Design

Appendix: About R

Bibliography

Index

Dummy View - NOT TO BE DELETED