Chapter 7, Problem 31E

(a)

To determine

To describe the relationship between the housing cost index and the median family income by state.

Explanation of Solution

The office of federal housing enterprise collects data on various aspects of housing cost around the U.S. And the scatterplot on housing cost index and the median family income is given. The correlation is also given as $0.65$ .

We can see that the relationship between the housing cost index and the median family income by state is that the association is positive, moderately strong and roughly straight with several states whose housing cost index seems high for their median income and one state whose housing cost index appears low given its median income.

(b)

To determine

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

Answer to Problem 31E

It will not change.

Explanation of Solution

The office of federal housing enterprise collects data on various aspects of housing cost around the U.S. And the scatterplot on housing cost index and the median family income is given. The correlation is also given as $0.65$ .

It is given if we standardized both the variables that is if we standardized both housing cost index and the median family income then, the correlation coefficient would remain the same as it does not affect the correlation coefficient.

(c)

To determine

To explain how would the correlation change if we had measured median family income in thousands of dollars instead of dollars.

Answer to Problem 31E

It will not change.

Explanation of Solution

The office of federal housing enterprise collects data on various aspects of housing cost around the U.S. And the scatterplot on housing cost index and the median family income is given. The correlation is also given as $0.65$ .

It is given if we had measured median family income in thousands of dollars instead 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 that affect the correlation coefficient if you were to include DC in the data set.

Answer to Problem 31E

Correlation would be lower.

Explanation of Solution

The office of federal housing enterprise collects data on various aspects of housing cost around the U.S. And the scatterplot on housing cost index and the median family income is given. The correlation is also given as $0.65$ .

If you were to include DC in the data set then DC would be a moderate outlier whose housing cost index is high for its median family income and it would lower the correlation slightly. So, the correlation would be lowered than $0.65$ .

(e)

To determine

To explain do these data provide proof that by raising the median income by state, the housing cost income would rise as a result or not.

Answer to Problem 31E

No.

Explanation of Solution

The office of federal housing enterprise collects data on various aspects of housing cost around the U.S. And the scatterplot on housing cost index and the median family income is given. The correlation is also given as $0.65$ .

No, these data does not provide proof that by raising the median income by state, the housing cost income would rise as a result because we can only say that higher median family income are associated with higher housing cost index and there may be other economic variables at work.