Whatโs my grade? In Professor Friedmanโs economics course, the correlation
between the studentsโ total scores prior to the final examination and their final exam scores is r = 0.6. The pre-exam totals for all students in the course have a mean of 280 and a standard deviation of 30. The final exam scores have a mean of 75 and a standard deviation of 8. Professor Friedman has lost Julieโs final exam but knows that her total before the exam was 300. He decides to predict her final exam score from her pre-exam total.
a. Find the equation for the least-squares regression line Professor Friedman should use to make this prediction.
b. Use the least-squares regression line to predict Julieโs final exam score.
c. Explain the meaning of the phrase โleast squaresโ in the context of this question.
d. Julie doesnโt think this method accurately predicts how well she did on the final exam. Determine r2. Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.