Statistics: Investigating Correlation

Objectives

• Students will recognize that the correlation coefficient describes the strength and direction of the linear association between two variables.
• Students will recognize that when two variables are highly linearly correlated, their correlation coefficient will be close to , and when they have little correlation, the correlation coefficient will be close to 0.
• Students will recognize that two variables with a high correlation coefficient might have a scatterplot that displays a nonlinear pattern.
• Students will recognize that correlation is not affected by the choice of x or y, that is, by the choice of which variable is explanatory and which is response.

Vocabulary

• correlation coefficient
• explanatory variable
• linear
• outlier
• response variable
• scatterplot

About the Lesson

This lesson involves investigating the connection between the scatterplot of bivariate data and the numerical value of the correlation coefficient.
As a result, students will:

• Consider a scatterplot of points that lie in a straight line and one whose points do not line in a straight line and interpret the correlation coefficient for each plot.
• Look at pairs of scatterplots to estimate which plot has the higher correlation coefficient.
• Move points to try to match a given correlation coefficient.
• Investigate a plot of ordered pairs and a plot of the inverse relation by inspecting the coordinates of the points and, by dragging the points in either plot, observing that the correlation coefficients are the same for both plots.