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)
Answer
Therefore, the percentage of the variation in \(y\) that can be explained by the variation in the values of \(x\) is \(\boxed{82.81\%}\).
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 \(\boxed{82.81\%}\).
