# Regression to the mean

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. *The least-squares line for predicting final exam score from midterm exam score was

y-hat = 46.6 + 0.41x. *

*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 exam?* (Hint: What is the predicted final score for the class mean midterm score x-bar?) This is an example of regression to the mean, the phenomenon that gave "regression" its name: students who do well on the midterm will on average do less well on the final, but still above the class mean.

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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. *The least-squares line for predicting final exam score from midterm exam score was

y-hat = 46.6 + 0.41x. *

*Octavio scores 10 points ...

#### Solution Summary

This solution explains how many points above a class mean should you predict a student will score on the final exam.