# faraway

1. Introduction
• Before You Start
• Initial Data Analysis
• When to Use Linear Modeling
• History
2. Estimation
• Linear Model
• Matrix Representation
• Estimating β
• Least Squares Estimation
• Examples of Calculating β
• Example
• QR Decomposition
• Gauss–Markov Theorem
• Goodness of Fit
• Identiﬁability
• Orthogonality
3. Inference
• Hypothesis Tests to Compare Models
• Testing Examples
• Permutation Tests
• Sampling
• Conﬁdence Intervals for β
• Bootstrap Conﬁdence Intervals
4. Prediction
• Conﬁdence Intervals for Predictions
• Predicting Body Fat
• Autoregression
• What Can Go Wrong with Predictions?
5. Explanation
• Simple Meaning
• Causality
• Designed Experiments
• Observational Data
• Matching
• Qualitative Support for Causation
6. Diagnostics
• Checking Error Assumptions
• Constant Variance
• Normality
• Correlated Errors - Finding Unusual Observations
• Leverage
• Outliers
• Inﬂuential Observations - Checking the Structure of the Model - Discussion
7. Problems with the Predictors
• Errors in the Predictors
• Changes of Scale
• Collinearity
8. Problems with the Error
• Generalized Least Squares
• Weighted Least Squares
• Testing for Lack of Fit
• Robust Regression
• M-Estimation
• Least Trimmed Squares
9. Transformation
• Transforming the Response
• Transforming the Predictors
• Broken Stick Regression
• Polynomials
• Splines
• More Complex Models
10. Model Selection
• Hierarchical Models
• Testing-Based Procedures
• Criterion-Based Procedures
• Summary
11. Shrinkage Methods
• Principal Components
• Partial Least Squares
• Ridge Regression
• Lasso
12. Insurance Redlining — A Complete Example
• Ecological Correlation
• Initial Data Analysis
• Full Model and Diagnostics
• Sensitivity Analysis
• Discussion
13. Missing Data
• Types of Missing Data
• Deletion
• Single Imputation
• Multiple Imputation
14. 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
15. One Factor Models
• The Model
• An Example
• Diagnostics
• Pairwise Comparisons
• False Discovery Rate
16. Models with Several Factors
• Two Factors with No Replication
• Two Factors with Replication
• Two Factors with an Interaction
• Larger Factorial Experiments
17. Experiments with Blocks
• Randomized Block Design
• Latin Squares
• Balanced Incomplete Block Design