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) Prediction equation is y^ = 30 + 0:60x. Determine predicted final exam score for student who has (i) midterm score = 100, (ii) midterm score = 50. Note that predicted final exam score regresses toward 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.