Linear Models with R

A Hands-On Way to Learning Data Analysis Part of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition. New to the Second Edition Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates Extensive use of the ggplot2 graphics package in addition to base graphics Like its widely praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R.

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 ObservationsChecking 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