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.
(source: Nielsen Book Data)
Publisher's Summary:
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 as well, all with their particular strengths and weaknesses. Lately, however, one such package has begun to rise above the others thanks to its free availability, its versatility as a programming language, and its interactivity. That software is R.In the first book that directly uses R to teach data analysis, Linear Models with R focuses on the practice of regression and analysis of variance. It clearly demonstrates the different methods available and more importantly, in which situations each one applies. It covers all of the standard topics, from the basics of estimation to missing data, factorial designs, and block designs, but it also includes discussion on topics, such as model uncertainty, rarely addressed in books of this type. The presentation incorporates an abundance of examples that clarify both the use of each technique and the conclusions one can draw from the results. All of the data sets used in the book are available for download from http://www stat.lsa.umich.edu/ faraway/LMR/.The author assumes that readers know the essentials of statistical inference and have a basic knowledge of data analysis, linear algebra, and calculus. The treatment reflects his view of statistical theory and his belief that qualitative statistical concepts, while somewhat more difficult to learn, are just as important because they enable us to practice statistics rather than just talk about it. (source: Nielsen Book Data)