What is the $r$-value of the following data, to three decimal places? \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 4 & 2 \\ \hline 5 & 9 \\ \hline 8 & 10 \\ \hline 9 & 12 \\ \hline 13 & 23 \\ \hline \end{tabular} A. -0.953 B. 0.908 C. -0.908 D. 0.953 SUBMIT

Step 1 ：We are given the following data pairs (x, y): (4, 2), (5, 9), (8, 10), (9, 12), (13, 23).

Step 2 ：We are asked to find the correlation coefficient, or r-value, of this data to three decimal places.

Step 3 ：The formula for the r-value is \(r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}\), where n is the number of data pairs, \(\sum xy\) is the sum of the product of each pair of data, \(\sum x\) and \(\sum y\) are the sums of the x and y data respectively, and \(\sum x^2\) and \(\sum y^2\) are the sums of the squares of the x and y data respectively.

Step 4 ：First, we calculate the necessary values for the formula: n = 5, \(\sum x\) = 39, \(\sum y\) = 56, \(\sum xy\) = 540, \(\sum x^2\) = 355, \(\sum y^2\) = 858.

Step 5 ：Substituting these values into the formula, we find that r = 0.953.

Step 6 ：Thus, the r-value of the given data, to three decimal places, is \(\boxed{0.953}\).