Let y = final exam score and x = midterm exam score. Suppose that the correlation is 0.70 and that the standard deviation is the same for each set of scores.
a. Using part b of the previous exercise and the relation between the slope and correlation, show that (ŷ - ) = 0.70(x - ).
b. Explain why this indicates that the predicted difference between your final exam grade and the class mean is 70% of the difference between your midterm exam score and the class mean. Your score is predicted to “regress toward the mean.” (The concept of regression toward the mean, which is responsible for the name of regression analysis, will be discussed in Section 12.2 .)