Bivariate Linear Regression

Week 3

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• if you need a refresher, first go through the Bivariate Correlation Review

Concepts

Here is a list of the main concepts you should be familiar with after this week:

Linear Regression

• equation of a line: x-intercept, y-intercept, slope
• finding the best fit line (using equations & using R’s lm() function)
• regression residuals
• model coefficients
• quantifying 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

Overview

This week we will introduce linear regression, which you might know as fitting a straight line to a set of data. In the lab this week you will work through some hands-on tasks in RStudio that illustrate correlation and regression.

1. Work through the readings below.
2. Review the week 3 slides
3. Attend the lab session to go through the Lab Component of Homework 3.
4. Complete the Home Component of Homework 3

We will use the following online textbooks:

• Answering questions with data by Matthew Crump, Danielle Navarro, & Jeffrey Suzuki
• Learning Statistics with R by Danielle Navarro (pdf version)

Required Readings

• 15.1 What is a linear regression model? in Learning Statistics with R
• 15.2 Estimating a linear regression model? in Learning Statistics with R
• you can skip Chapter 15.3 Multiple linear regression, we will be doing that next week
• 15.4 Quantifying the fit of the regression model? in Learning Statistics with R
• 15.5 Hypothesis tests for regression models in Learning Statistics with R
• you can skip Chapter 15.6 Testing the significance of a correlation, that should be already familiar to you (if not, review it)
• 15.7 Regarding regression coefficients 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

Additional supporting materials

• Chapter 3.5 Regression: A mini intro in Answering questions with data
• Intro to Linear Regression video playlist (YouTube)