Regression Models for Data Science in R A companion book for the Coursera Regression Models class

Table of Contents
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 swiss dataset
	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!