Chapter 3.1, Problem 23E

(a)

To determine

To explain why it is not correct to say that the correlation is $0.87$ mg/cal.

Explanation of Solution

According to this question, we have to find out that why it is not correct to say that the correlation is $0.87$ mg/cal. Thus, we cannot say that the correlation is $0.87$ mg/cal because we then note that we assigned the units “mg/cal” to the correlation. However, there are never units associated with correlation. Thus, this statement is not true.

(b)

To determine

To explain what would happen to the correlation if the variables were reversed on the scatterplot.

Answer to Problem 23E

The correlation remains the same.

Explanation of Solution

According to the question, we have to find out what would happen to the correlation if the variables were reversed on the scatterplot. As we know that the correlation measures the amount of linearity present between two variables. Thus, if the variables were reversed on the scatterplot then the amount of linearity that is present between the two variables is unaffected and thus the correlation is unaffected as well.

(c)

To determine

To explain what would happen to the correlation if sodium was measured in grams instead of milligrams.

Answer to Problem 23E

The correlation will remain the same.

Explanation of Solution

According to the question, we have to find out what would happen to the correlation if sodium was measured in grams instead of milligrams. As we know that the correlation measures the amount of linearity present between two variables. Thus, if sodium was measured in grams instead of milligrams then this does not affect the association between the variables as they will still have the same relationship. Thus, the amount of linearity in the association between the variables then remains unchanged as well and thus the correlation will remain unchanged as well.