Chapter 12, Problem AP4.27CPT

To determine

To find out which of the following is the correct value of the correlation and its corresponding interpretation.

Answer to Problem AP4.27CPT

Option (d) is the correct option.

Explanation of Solution

Park rangers are interested in estimating the weight of the bears that inhabit their state. The output of this data is given in the question. The coefficient of determination $r^2$ is given in the computer output following “R-Sq” as:

  $r^2=94.7\%=0.947$

The correlation coefficient is the positive or negative square root of the coefficient of determination. The pattern in the scatterplot slopes upward which implies that there is a positive relationship between the variables and thus the correlation coefficient needs to be positive. Thus, it is calculated as:

  $\begin{array}{l}r=+\sqrt{r^2}\\ =+\sqrt{0.947}\\ =0.973\end{array}$

Since the correlation coefficient is close to one, the linear relationship between the variables is strong and thus the option (d) is the correct option.