# Question

For students who take Statistics 101 at Lake Wobegon College in Minnesota, both the midterm and final exams have mean = 75 and standard deviation = 10. The professor explores using the midterm exam score to predict the final exam score.

The regression equation relating y = final exam score to x = midterm exam score is ŷ = 30 + 0.60x.

a. Find the predicted final exam score for a student who has (i) midterm score = 100, (ii) midterm score = 50. In each case the predicted final exam score regresses toward the mean of 75. (This is a property of the regression equation that is the origin of its name, as Chapter 12 will explain.)

b. Show that the correlation equals 0.60, and interpret it.

The regression equation relating y = final exam score to x = midterm exam score is ŷ = 30 + 0.60x.

a. Find the predicted final exam score for a student who has (i) midterm score = 100, (ii) midterm score = 50. In each case the predicted final exam score regresses toward the mean of 75. (This is a property of the regression equation that is the origin of its name, as Chapter 12 will explain.)

b. Show that the correlation equals 0.60, and interpret it.

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