example: Which of the following statements best describes the scatterplot pictured? I. A line might fit the data well.
II. The variables are positively associated.
III. The variables are negatively associated.
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
solution: e is correct. The data look as though a line might be a good model, and the y -variable
decreases as the x- variable increases so that they are negatively associated.Correlation
We have seen how to graph two-variable data in a scatterplot. Following the pattern we set in the
previous chapter, we now want to do some numerical analysis of the data in an attempt to understand the
relationship between the variables better.
In AP Statistics, we are primarily interested in determining the extent to which two variables are linearly
associated. Two variables are linearly related to the extent that their relationship can be modeled by a
line. Sometimes, and we will look at this more closely later in this chapter, variables may not be linearly
related but can be transformed in such a way that the transformed data are linear. Sometimes the data are
related but not linearly (e.g., the height of a thrown ball, t seconds after it is thrown, is a quadratic
function of the number of seconds elapsed since it was released).
The first statistic we have to quantify a linear relationship is the Pearson product moment correlation,