Interest rates and mortgages again. In given Exercise, we saw a plot of total mortgages in the United States (in millions of 2005 dollars) versus the interest rate at various times over the past 26 years. The correlation is r =-0.84. The mean mortgage amount is $151.9 million and the mean interest rate is 8.88%. The standard deviations are $23.86 million for mortgage amounts and 2.58% for the interest rates.
a) Is a regression model appropriate for predicting mortgage amount from interest rates? Explain.
b) What is 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 20%?
d) Do you have any reservations about your prediction in part c?
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?
Exercise :
Interest rates and mortgages. Since 1980, average mortgage interest rates have fluctuated from a low of under 6% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that's offered? Here is a scatterplot of Total Mortgages in the United States (in millions of 2005 dollars) versus Interest Rate at various times over the past 26 years. The correlation is -20.84.
a) Describe the relationship between Total Mortgages and Interest Rate.
b) If we standardized both variables, what would the correlation coefficient between the standardized variables be?
c) If we were to measure Total Mortgages in thousands of dollars instead of millions of dollars, how would the correlation coefficient change?
d) Suppose in another year, interest rates were 11% and mortgages totaled $250 million. How would including that year with these data affect the correlation coefficient?
e) Do these data provide proof that if mortgage rates are lowered, people will take out more mortgages? Explain.