Regression Models for Data Science in R
This book is 90% complete
Last updated on 20190413
About the Book
The ideal reader for this book will be quantitatively literate and has a basic understanding of statistical concepts and R programming. The student should have a basic understanding of statistical inference such as contained in https://leanpub.com/LittleInferenceBook/. The book gives a rigorous treatment of the elementary concepts of regression models from a practical perspective. After reading the book and watching the associated videos, students will be able to perform multivariable regression models and understand their interpretations.
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The Book+Videos+Code
This is the book, plus the videos, plus the video solutions. All of the videos are available on YouTube as well. The book plus lecture note github repos are included as well.
Includes:
Video lectures
These are the video lectures associated with the book. They are also available on YouTube and Coursera.
Lecture notes and code
This is the github repo zipped up as one entity. You can get this off of github if you'd like. It also includes the book repo.
PDF
EPUB
MOBI
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The Book+Code+Lecture Videos+Solution Videos
This is the book, the github repos (lecture notes and book) plus the video lectures plus the video HW solutions. All are available elsewhere for free (github and YouTube).
Includes:
Video lectures
These are the video lectures associated with the book. They are also available on YouTube and Coursera.
Lecture notes and code
This is the github repo zipped up as one entity. You can get this off of github if you'd like. It also includes the book repo.
Video HW solutions.
This is the video homework solutions. These are also all available on YouTube.
PDF
EPUB
MOBI
APP
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 underfitting 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
 Meanvariance relationship
 Rates
 Exercises

Bonus material
 How to fit functions using linear models
 Notes
 Harmonics using linear models
 Thanks!
 Notes
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