# Lesson 12: Correlation & Simple Linear Regression

In Lesson 11 we examined relationships between two categorical variables with the chi-square test of independence. In this lesson, we will examine the relationships between two quantitative variables with correlation and simple linear regression. **Quantitative variables** have numerical values with magnitudes that can be placed in a meaningful order. You were first introduced to correlation and regression in section 3.4. We will review some of the same concepts again, and we will see how we can test for the statistical significance of a correlation or regression slope using the t distribution.

In addition to reading section 9.1 in the Lock^5 textbook this week, you may also want to go back to review sections 2.5 and 2.6 where scatterplots, correlation, and regression were first introduced.

### Lesson 12 Learning Objectives

Upon completion of this lesson, you should be able to do the following:

- identify situations in which correlation or regression analyses are appropriate.
- within a given scenario, identify the explanatory and response variables.
- interpret scatterplots.
- compute and interpret Pearson
*r*correlation coefficients. - compute and interpret a simple linear regression model (i.e., y-intercept and slope).
- compute and interpret a residual from a simple linear regression model.
- explain how outliers can influence correlation and regression analyses.
- compute and interpret the coefficient of determination (R
^{2}). - test for the statistical significance of a correlation or slope using the t distribution.