Midterm–final correlation For students who take Statistics 101 at Lake Wobegon College in Minnesota, both the midterm and final exams have mean = 75 and standard deviation = 10. The professor explores using the midterm exam score to predict the final exam score.

The regression equation relating y = final exam score to x = midterm exam score is yn = 30 + 0.60x.

a. Find the predicted final exam score for a student who has (i) midterm score = 100, (ii) midterm score = 50.

Note that in each case the predicted final exam score regresses toward the mean of 75. (This is a property of the regression equation that is the origin of its name, as Chapter 12 will explain.)

b. Show that the correlation equals 0.60 and interpret it. (Hint: Use the relation between the slope and correlation.)