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.

First, examine whether the score on the freshmen final exam predicts sophomore GPA.

(a) Convert the test scores (X) and the sophomore averages (Y) to z scores.

(b) By inspection of the paired z scores, estimate whether the correlation between these variables is positive, negative or zero. Then verify your estimate by computing r using the z score difference formula.

(c) Now recompute r_xy by the Z score product formula to verify the result in (a) is the “same.” (Note that, due to rounding, the result may not be exact. Hint: In this case, it differs by approximately .06.)

(d) In one sentence, what does the result of the r_xy correlation coefficient mean to the dean?