For students who take Statistics 101 at Lake Wobegon College in Minnesota, both X = midterm exam score and Y = nal exam score have mean = 75 and standard deviation = 10.
a) The prediction equation is y^ = 30 + 0:60x. Find the predicted nal exam score for a student who has (i) midterm score = 100, (ii) midterm score = 50. Note that the predicted nal exam score regresses toward the mean.
b) Show that the correlation equals 0.60.
c) If instead, y^ = x, show that r = 1.0
d) If instead, y^ = 75, show that r = 0.0.