Linear Models with R

Books on regression and the analysis of variance abound many are introductory, many are theoretical. While most of them do serve a purpose, the fact remains that data analysis cannot be properly learned without actually doing it, and this means using a statistical software package. There are many of these to choose from, all with their particular s

Table of Contents:
INTRODUCTION Before b Initial Data Analysis When to Use Regression Analysis History ESTIMATION Linear Model Matrix Representation Estimating b Least b Examples of Calculating Gauss-Markov Theorem Goodness of Fit Example Identifiability INFERENCE Hypothesis Tests to compare models Testing Examples Permutation tests Confidence Intervals for b Confidence Intervals for Predictions Designed Experiments Observational Data Practical Difficulties DIAGNOSTICS Checking Error Assumptions Finding Unusual Observations Checking the Structure of the Model PROBLEMS WITH THE PREDICTORS Errors in 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 VARIABLE SELECTION Hierarchical Models Testing-based Procedures Criterion-based procedures Summary SHRINKAGE METHODS Principal Components Partial Least Squares Ridge Regression STATISTICAL STRATEGY AND MODEL UNCERTAINTY Strategy An Experiment in Model Building Discussion CHICAGO INSURANCE REDLINING - A COMPLETE EXAMPLE Ecological Correlation Initial Data Analysis Initial model and Diagnostics Transformation and Variable Selection Discussion MISSING DATA ANALYSIS OF COVARIANCE A Two-Level Example Coding Qualitative Predictors A Multi-Level Factor Example ONE-WAY ANOVA The Model An Example Diagnostics Pairwise Comparisons FACTORIAL DESIGNS Two-Way Anova Two-Way Anova with One Observation per Cell Two-Way Anova with more than One Observation per Cell Larger Factorial Experiments BLOCK DESIGNS Randomized Block design Latin Squares Balanced Incomplete Block design APPENDICES R installation, Functions and Data Quick Introduction to R BIBLIOGRAPHY INDEX