Regression Models for Data Science in R
A companion book for the Coursera Regression Models class
About
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
Minimum price
Suggested price14ドル.99This 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.
$14.99
- Video lecturesThese are the video lectures associated with the book. They are also available on YouTube and Coursera.
- Lecture notes and codeThis 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.
The Book
Minimum price
Suggested price14ドル.99This is just the boook.
Free!
This book is also available in the following packages:
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).
- Video lecturesThese are the video lectures associated with the book. They are also available on YouTube and Coursera.
- Lecture notes and codeThis 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.
- Minimum price
- 19ドル.99
- Suggested price
- 24ドル.99
- Video lectures
Contents
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!
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