Regression Models for Data Science in R
This book is 90% complete
Last updated on 2019-04-13
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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About the Author
Packages
The Book
This is just the boook.
PDF
EPUB
MOBI
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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
APP
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
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!
- Notes
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