We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period.17 The least-squares line for predicting final exam score from midterm-exam score was y = 46.6 + 0.41x. (Both exams have a 100-point scale.)
Octavio scores 10 points above the class mean on the midterm. How many points above the class mean do you predict that he will score on the final? (Hint: Use the fact that the least-squares line passes through the point (, ) and the fact that Octavio's midterm score is + 10.) This is another example of regression to the mean: students who do well on the midterm will on the average do less well, but still above average, on the final.