Regression Models for Data Science in R

Regression Models for Data Science in R

Brian Caffo
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Table of Contents

Regression Models for Data Science in R

  • 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
    • 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
Regression Models for Data Science in R/Overview

Regression Models for Data Science in R

Course overview

This is a companion book to the Coursera Regression Models class as part of the Data Science Specialization

17 chapters
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The Book

Regression Models for Data Science in R17 chapters

Begin ›
  1. Preface

  2. Introduction

  3. Notation

  4. Ordinary least squares

  5. Regression to the mean

  6. Statistical linear regression models

  7. Residuals

  8. Regression inference

  9. Multivariable regression analysis

  10. Multivariable examples and tricks

  11. Residuals, variation, diagnostics

  12. Multiple variables and model selection

  13. Generalized Linear Models

  14. Binary GLMs

  15. Count data

  16. Bonus material

  17. Notes