To find the [tex]$r$[/tex]-value (the correlation coefficient) of the given data, we need to follow these steps:
1. List the paired data points:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
4 & 26 \\
5 & 11 \\
8 & 13 \\
9 & 2 \\
13 & 1 \\
\end{array}
\][/tex]
2. Calculate the means [tex]$\bar{x}$[/tex] and [tex]$\bar{y}$[/tex]:
[tex]\[
\bar{x} = \frac{4 + 5 + 8 + 9 + 13}{5} = \frac{39}{5} = 7.8
\][/tex]
[tex]\[
\bar{y} = \frac{26 + 11 + 13 + 2 + 1}{5} = \frac{53}{5} = 10.6
\][/tex]
3. Calculate the sums of squares and cross-products:
[tex]\[
S_{xx} = \sum (x_i - \bar{x})^2
\][/tex]
[tex]\[
S_{yy} = \sum (y_i - \bar{y})^2
\][/tex]
[tex]\[
S_{xy} = \sum (x_i - \bar{x})(y_i - \bar{y})
\][/tex]
4. Calculate the correlation coefficient [tex]$r$[/tex]:
[tex]\[
r = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}}
\][/tex]
After performing all the necessary calculations step-by-step, we find that the [tex]$r$[/tex]-value of the given data, rounded to three decimal places, is:
[tex]\[
r \approx -0.828
\][/tex]
Thus, the correct answer is:
A. -0.828
