In Chapter 6, Exercise 40, we saw a plot of mortgages in the United States (in trillions of 2013 dollars) vs. the interest rate at various times over the past 25 years. The correlation is r = -0.80. The mean mortgage amount is $3,926 T and the mean interest rate is 7.194%. The standard deviations are $1,515 T for mortgage amounts and 2.055% for the interest rates.

a) Is a regression model appropriate for predicting mortgage amount from interest rates? Explain.
b) Regardless of your answer to a), find the equation that predicts mortgage amount from interest rates?
c) What would you predict the mortgage amount would be if the interest rates climbed to 13%?
d) Do you have any reservations about your prediction in part c? Explain.
e) If we standardized both variables, what would be the regression equation that predicts standardized mortgage amount from standardized interest rates?
f) If we standardized both variables, what would be the regression equation that predicts standardized interest rates from standardized mortgage amount?

10 12 Interest Rate (%)