Chapter 7, Problem 32E

(a)

To determine

To describe the relationship between the total mortgages and interest rates.

Explanation of Solution

It is given that in question a scatterplot of total mortgages and interest rates at various times over the past years. And also the correlation between the total mortgages and interest rate is $-0.84$ .

We can see that the relationship between the total mortgages and the interest rates is that the association between the total mortgages and the interest rates isnegative, linear and moderately strong. And by looking at the scatterplot, we can see that the graph is decreasing downward sloping as the dots are in the downward direction.

(b)

To determine

To explain what would the correlation coefficient between the standardized variables be.

Answer to Problem 32E

It will not change.

Explanation of Solution

It is given that in question a scatterplot of total mortgages and interest rates at various times over the past years. And also the correlation between the total mortgages and interest rate is $-0.84$ .

It is given if we standardized both the variables that is if we standardized both total mortgage and interest rate then, the correlation coefficient would remain the same as it does not affect the correlation coefficient and we would put them in z -scores only.

(c)

To determine

To explain how would the correlation change if we had measured total mortgages in thousands of dollars instead of millions of dollars.

Answer to Problem 32E

It will not change.

Explanation of Solution

It is given that in question a scatterplot of total mortgages and interest rates at various times over the past years. And also the correlation between the total mortgages and interest rate is $-0.84$ .

It is given if we had measured total mortgages in thousands of dollars instead of millions of dollars, the correlation coefficient would remain the same as it does not affect the correlation coefficient as it is not affected by the units of measurements.

(d)

To determine

To explain how would includingthat year with these data affect the correlation coefficient.

Answer to Problem 32E

Correlation would be lower.

Explanation of Solution

It is given that in question a scatterplot of total mortgages and interest rates at various times over the past years. And also the correlation between the total mortgages and interest rate is $-0.84$ .

It is given that in the year that is to be added, interest rate were $11\%$ and mortgage total $\$250$ million. If you were to that year with these data then the correlation coefficient will be affected with it as the scatterplot would be weaker because the point would be farther away from it.

(e)

To determine

To explain do these data provide proof that if mortgage rates are lowered people will take out more mortgages or not.

Answer to Problem 32E

No.

Explanation of Solution

It is given that in question a scatterplot of total mortgages and interest rates at various times over the past years. And also the correlation between the total mortgages and interest rate is $-0.84$ .

No, these data does not provide proof that that if mortgage rates are lowered people will take out more mortgagesbecause the correlation coefficient does not cause causation.