Question

The correlation coefficient (r) between the number of volunteers x and the numberof bags of trash collected y is 0.642.What percent of the variation in the number of bags of trash collected can bexplained by differences in the number of volunteers?

Answer 1

Given the coefficient of correlation and coefficient of determination relationship as

$\text{ coefficient of }\det \text{ermintaion}=r^2$

Since,

$r=0.642$

Then,

$\begin{gathered} \text{ Coefficient of determination=0.642}^2 \\ =0.4122 \end{gathered}$

Thus, the percentage of variation will be;

$\begin{gathered} 0.4122\times100\text{ \%} \\ \Rightarrow41.22\text{ \%} \end{gathered}$

Hence, the percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers is 41.22 %