Preface
- About this book
- About the cover
Introduction
- Before beginning
- Regression models
- Motivating examples
- Summary notes: questions for this book
- Exploratory analysis of Galton’s Data
- The math (not required)
- Comparing children’s heights and their parent’s heights
- Regression through the origin
- Exercises
Notation
- Some basic definitions
- Notation for data
- The empirical mean
- The empirical standard deviation and variance
- Normalization
- The empirical covariance
- Some facts about correlation
- Exercises
Ordinary least squares
- General least squares for linear equations
- Revisiting Galton’s data
- Showing the OLS result
- Exercises
Regression to the mean
- A historically famous idea, regression to the mean
- Regression to the mean
- Exercises
Statistical linear regression models
- Basic regression model with additive Gaussian errors.
- Interpreting regression coefficients, the intercept
- Interpreting regression coefficients, the slope
- Using regression for prediction
- Example
- Exercises
Residuals
- Residual variation
- Properties of the residuals
- Example
- Estimating residual variation
- Summarizing variation
- R squared
- Exercises
Regression inference
- Reminder of the model
- Review
- Results for the regression parameters
- Example diamond data set
- Getting a confidence interval
- Prediction of outcomes
- Summary notes
- Exercises
Multivariable regression analysis
- The linear model
- Estimation
- Example with two variables, simple linear regression
- The general case
- Simulation demonstrations
- Interpretation of the coefficients
- Fitted values, residuals and residual variation
- Summary notes on linear models
- Exercises
Multivariable examples and tricks
- Data set for discussion
- Simulation study
- Back to this data set
- What if we include a completely unnecessary variable?
- Dummy variables are smart
- More than two levels
- Insect Sprays
- Further analysis of the
swissdataset - Exercises
Adjustment
- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Some final thoughts
- Exercises
Residuals, variation, diagnostics
- Residuals
- Influential, high leverage and outlying points
- Residuals, Leverage and Influence measures
- Simulation examples
- Example described by Stefanski
- Back to the Swiss data
- Exercises
Multiple variables and model selection
- Multivariable regression
- The Rumsfeldian triplet
- General rules
- R squared goes up as you put regressors in the model
- Simulation demonstrating variance inflation
- Summary of variance inflation
- Swiss data revisited
- Impact of over- and under-fitting on residual variance estimation
- Covariate model selection
- How to do nested model testing in R
- Exercises
Generalized Linear Models
- Example, linear models
- Example, logistic regression
- Example, Poisson regression
- How estimates are obtained
- Odds and ends
- Exercises
Binary GLMs
- Example Baltimore Ravens win/loss
- Odds
- Modeling the odds
- Interpreting Logistic Regression
- Visualizing fitting logistic regression curves
- Ravens logistic regression
- Some summarizing comments
- Exercises
Count data
- Poisson distribution
- Poisson distribution
- Linear regression
- Poisson regression
- Mean-variance relationship
- Rates
- Exercises
Bonus material
- How to fit functions using linear models
- Notes
- Harmonics using linear models
- Thanks!