since 1985, average mortgage interest rates have fluctuated from a low of under
ID: 3127897 • Letter: S
Question
since 1985, 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 mortgage loan amount in the united states (in thousands of dollars) versus interest rate at various times over the past 26 years. The correlation is -0.86. (a) describe th erelationship between mortgage loan amount 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 mortgage loan amount in hundres of dollars instead of thousands of dollars, how would the correlation coefficient change? (d) suppose in another year, interest rates were 11% and mortgages totaled $250 Thousand. 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 larger mortgages? explain.
Explanation / Answer
a) As the correlation coefficient is -0.86, SO there is a negative relation between the amount of money people borrow and the interest rate that's offered
b) As the standardizing a variable does not change its magnitude. and he correlation coefficient dependents on the magnitude of the varaible. So the correlation coefficent will remain the same -0.86
c) Since Correlation Coefficient is independent of the change of origin and scale. So there will be no change in
Correlation Coefficient
d) There is no effect as Correlation Coefficient is independent of the change of origin and scale
e) Since there is a negative correlation between the two so with the decrease in one varaible there will e an increase in another. That is people will take out larger mortgages if mortgage rates are lowered
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