For students who take Statistics 101 at Lake Wobegon College in Minnesota, both x = midterm exam score and y = final exam score have mean = 75 and standard deviation = 10.

(a) The prediction equation is ˆy = 30 + 0.60x. Find the predicted final exam score for a student who has

(i) midterm score = 100, (ii) midterm score = 50. Note that the predicted final exam score regresses from the midterm score toward the mean.

(b) Show that the correlation equals 0.60.

(c) If instead, ˆy = x, show that r = 1.0.

(d) If instead, ˆy = 75 (i.e., slope = 0), show that r = 0.0.