Chapter 6, Problem 40E

Interest rates and mortgages 2015 Since 1985, average mortgage interest rates have fluctuated from a low of nearly 3% 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 Mortgage Loan Amount in the United States (in trillions of dollars) versus yearly Interest Rate since 1985. The correlation is -0.85.

1. a) Describe the relationship between Mortgage Loan Amount and Interest Rate.
2. b) If we standardized both variables, what would the correlation coefficient between the standardized variables be?
3. c) If we were to measure Mortgage Loan Amount in billions of dollars instead of trillions of dollars, how would the correlation coefficient change?
4. d) Suppose that next year, interest rates were 11% and mortgages totaled $60 trillion. How would including that year with these data affect the correlation coefficient?
5. e) Do these data provide proof that if mortgage rates are lowered, people will take out larger mortgages? Explain.