Linear Regression II & Intro to Multiple Regression

Week 5

Concepts

Linear Regression

• how to quantify the fit of a regression line using \(R^{2}\) and \(s_{est}\)
• using a regression line (linear model) for prediction
• confidence intervals on model coefficients
• testing the statistical significance of a linear regression model
• linear regression with non-linear terms

Multiple Regression

• the multiple regression equation
• quantifying the fit using \(R^{2}\) and \(s_{est}\)
• meaning of each model coefficient (weight)

Readings

We will be using the textbook Learning Statistics with R by Danielle Navarro. (pdf version) We will also be using the textbook OpenIntro Statistics.
Both are made available online, free.

Required Readings

Linear Regression

• 15.7 Regarding regression coefficients in Learning Statistics with R
• 15.5 Hypothesis tests for regression models in Learning Statistics with R
• 15.8 Assumptions of regression in Learning Statistics with R
• 15.9 Model checking in Learning Statistics with R
• Chapter 8 “Introduction to linear regression” of OpenIntro Statistics

Multiple Regression

• 15.3 Multiple linear regression in Learning Statistics with R
• Chapter 9 “Multiple and logistic regression” of OpenIntro Statistics (you can ignore 9.5 “Introduction to logistic regression” for now)

Additional supporting materials

• Intro to Linear Regression playlist (YouTube)