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 P
omona 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 mid-term exam score was γ=46.6 + 0.41x. Octavio scores 10 points above the clas mean on the midterm. How many points above the class mean do you predict that he will score on the final. (Hint: what is the predicted final-exam score for the class mean midterm score of 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.)
To convert a mixed number into an improper fraction, you can multiply the denominator of the fraction by the whole number. Then, you add the product with the numerator to get the new numerator. The denominator remains the same.
