Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as
and the $r = 0.91$ .
$y = 55.29 x + 52.09$

What percentage of the variation in $y$ can be explained by the variation in the values of $x$ ?
$r^{2} =$
\% (Report exact answer, and do not enter the \% sign)

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Therefore, the percentage of the variation in $y$ that can be explained by the variation in the values of $x$ is $82.81 %$ .

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Step 1 ：Given the correlation coefficient $r = 0.91$ .

Step 2 ：The percentage of the variation in $y$ that can be explained by the variation in the values of $x$ is given by the square of the correlation coefficient, $r^{2}$ .

Step 3 ：Calculate $r^{2}$ by squaring the correlation coefficient.

Step 4 ： $r^{2} = (0.91)^{2} = 0.8281$ .

Step 5 ：Therefore, the percentage of the variation in $y$ that can be explained by the variation in the values of $x$ is $82.81 %$ .

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