Lesson 12: Correlation & Simple Linear Regression

Objectives

Upon successful completion of this lesson, you should be able to:

  • Construct a scatterplot using Minitab Express and interpret it
  • Identify the explanatory and response variables in a given scenario
  • Identify situations in which correlation or regression analyses are appropriate
  • Compute Pearson r using Minitab Express, interpret it, and test for its statistical significance
  • Construct a simple linear regression model (i.e., y-intercept and slope) using Minitab Express, interpret it, and test for its statistical significance
  • Compute and interpret a residual given a simple linear regression model
  • Compute and interpret the coefficient of determination (R2)
  • Explain how outliers can influence correlation and regression analyses
  • Explain why extrapolation is inappropriate

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 Lesson 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 Lock5 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.