The following table presents monthly interest rates, in percent, for 30-year and 15-year fixed-rate mortgages, for a recent year.

a. Construct a scatterplot of the 15-year rate (y) versus the 30-year rate (x).

b. Compute the correlation coefficient between 30-year and 15-year rates.

c. When the 30-year rate is below average, would you expect the 15-year rate to be above or below average?
Explain.

d. Which of the following is the best interpretation of the correlation coefficient?
i. When a bank increases the 30-year rate, that causes the 15-year rate to rise as well.
ii. Interest rates are determined by economic conditions.
When economic conditions cause 30-year rates to increase, these same conditions cause 15-year rates to increase as well.
iii. When a bank increases the 15-year rate, that causes the 30-year rate to rise as well.

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30-Year 15-Year 30-Year 15-Year 3.92 3.20 3.55 2.85 3.89 3.16 3.60 2.86 3.95 3.20 3.47 2.78 3.91 3.14 3.38 2.69 3.80 3.03 3.35 2.66 3.68 2.95 3.35 2.66