Question: A college dean wants to predict sophomore grade point average for first-semester freshmen based on class attendance in order to identify students who may benefit from a counseling program. After students have been in school for one semester, the dean obtains their final examination average for the first semester (based on a total of 100 points) and also obtains the number of classes students missed in the semester. She waits a hear and a half, and then obtains their sophomore grade point average after the students complete their second year.

In a real study, a large sample would be desirable for this study; however, for the purpose of learning how to apply the correlation and regression procedures that are used, while also keeping the computations within reason, we are going to assume the dean has a sample of the seven students listed on the table below. Use this data set to perform the computations below.

Next, examine how strongly freshmen’s absences (C) predict their sophomore GPA (Y).

(a) Compute r_cy using the raw score computing formula, first computing all the smaller values that you need to plug into the formula.

(b) In one sentence, what does the r_cy correlation coefficient signify to the dean?