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 ŷ = 30 + 0.60x.
a. Find the predicted final exam score for a student who has (i) midterm score = 100, (ii) midterm score = 50. 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.