Question

question 10
using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. the regression equation is reported as
$y = -71.65x + 64.17$
and the $r=-0.762$.
what proportion of the variation in y can be explained by the variation in the values of x?
$r^{2}=$
report answer as a percentage accurate to one decimal place.

Explanation:

Step1: Square the correlation coefficient

Given \( r = - 0.762\), we calculate \(r^{2}\).

$$r^{2}=(-0.762)^{2}$$

Step2: Convert to percentage

$$r^{2}=0.580644$$

To convert to percentage, multiply by \(100\).

$$r^{2}=0.580644\times100 = 58.1\%$$

Answer:

\(58.1\%\)