Bivariate Correlation & Intro to Linear Regression

Week 4

Concepts

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

Bivariate Correlation

• correlation vs causation
• correlation strength vs correlation direction
• covariation
• Pearson’s r
• random correlations & the role of sample size

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

Overview

This week we will work through bivariate correlation—what it means, and how to compute it. We will also 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 4 slides
3. Attend the lab session to go through the Lab Component of Homework 4.
4. Complete the Home Component of Homework 4

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)

Requried Readings

Correlation

• read Chapter 3 Correlation sections 3.1–3.4 & 3.6 in Answering questions with data
• optional: also read Chapter 5.7 Correlations in Learning Statistics with R

Regression

• read Chapter 15.1 What is a linear regression model? in Learning Statistics with R
• read Chapter 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
• read Chapter 15.4 Quantifying the fit of the regression model? in Learning Statistics with R

Additional supporting materials

• Chapter 3.5 Regression: A mini intro in Answering questions with data