Question

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 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.)

Answer 1

Using the model equation, the predicted mean score on the final given a score of 10 points above the class mean in the mid term exam is 50.7

The Least - Square Regression equation which models the relationship between midterm and final exam score is :

• γ=46.6 + 0.41x

x = 10 points ; substitute the value of x = 10 into the regression equation ;

γ=46.6 + 0.41(10)

γ=46.6 + 4.1

γ = 50.7

The number of points above the mean he'll score in the final exam is predicted to be 50.7

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