In this lesson, students use technology to compute the correlation coefficient. Then they use it to categorize relationships between variables as strong or weak. A strong relationship is a relationship between two numerical variables that is represented very well by a linear model. A weak relationship is not represented very well by a linear model. Students also use the sign of the correlation coefficient to categorize relationships as positive or negative. In general, when the variables increase together, they have a positive relationship. If an increase in one variable’s data tends to be paired with a decrease in the other variable’s data, the variables have a negative relationship.

When students use the value of the correlation coefficient to describe the relationship between two variables, they are looking for and making use of structure (MP7). To make sense of the relationship between variables, students reason abstractly and quantitatively (MP2). When students examine relationships to think about correlations, they also consider additional variables that might have an influence on any trends they see. Deciding which variables need to be included is a part of the process of modeling with mathematics (MP4).