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 -0.84.

For these data Kendall’s tau is -0.61. Does that provide proof that if mortgage rates are lowered, people will take out more mortgages? Explain what Kendall’s tau says and does not say.

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Total Mortgage (millions of $) 200 180 160 40 140 120 + 6 8 10 Interest Rate (%) 12 14