Reconsider the previous exercise.
a. Determine the predicted score on Test 3 for a student who scores 55 on Test 2.
b. Determine the predicted score on Test 3 for a student who scores 95 on Test 2.
c. Of the two students in parts (a) and (b), which student is predicted to achieve a higher score on Test 3 than he or she scored on Test 2? Which student is predicted to achieve a lower score on Test 3 than he or she scored on Test 2? (This phenomenon is known as the regression effect.)

Data from previous exercise

The following scatterplot represents scores on Test 2 and Test 3 in Introductory Statistics for a random sample of students.

The regression equation for these data is ŷ = 55.2 + 0.3708x, where x is the score on Test 2 and yˆ is the expected score on Test 3. The mean for Test 2 was 79.80 and the mean for Test 3 was 84.80.

100 90 80 70 60 50 50 70 80 90 100 Test 2 Test 3