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. Assume that both the midterm and final exam were scored out of 100 points.

a. State the equation of the least-squares regression line if each student scored the same on the midterm and the final.

b. The actual least-squares line for predicting final-exam score y from midterm-exam score x was ŷ = 46.6 + 0.41x. Predict the score of a student who scored 50 on the midterm and a student who scored 100 on the midterm.

c. Explain how your answers to part (b) illustrate regression to the mean.