Question

In each of Exercises 4.169 and 4.170,

a. construct a scatterplot for the data.

b. decide whether using the rank correlation coefficient is reasonable.

c. decide whether using the linear correlation coefficient is reasonable.

d. find and interpret the rank correlation coefficient.
The coefficient of determination of a set of data points is $0.716$.

a. Can you determine the linear correlation coefficient? If yes, obtain it. If no, why not?

b. Can you determine whether the slope of the regression line is positive or negative? Why or why not?

c. If we tell you that the slope of the regression line is negative, can you determine the linear correlation coefficient? If yes, obtain it. If no, why not?

Short answer

The answers for the various subparts have been given below.

Step-by-step solution

Step 1. Given Information

The coefficient of determination of a set of data points is$0.716$.

Step 2. The answer of (a)

The given coefficient of determination of a set of data points is$r^2=0.716$.
Despite of having the coefficient of determination $\left(r^2\right)$, we don't need to determine the linear correlation coefficient $\left(r\right)$because from the coefficient of determination we can't say about the existence of linear relationship between the given variables.

Step 3. The answer of (b)

Despite of having the coefficient of determination $\left(r^2\right)$,we don't need to determine the sign of the slope of the regression line because $r=\pm \sqrt{r^2}$.

Step 4. The answer of (c)

Despite of having the value of the coefficient of determination and the sign of slope as negative, we are not sure about the existence of the linear relationship between the variable. Hence, the linear correlation coefficient cannot be determined.

Step 5. The answer of (d)

Despite of having the value of the coefficient of determination and the sign of slope as positive, we are not sure about the existence of the linear relationship between the variable. Hence, the linear correlation coefficient cannot be determined