Question

The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654

What percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers?

Answer 1

42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.

Explanation:

The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654

For finding the percent of the variation in one variable explained by the other variable, we just need to take square of the correlation coefficient.

Here,
`r=0.654`

So,
`r^2 = (0.654)^2 = 0.427716`

Now, for converting it into percentage, we will multiply it by 100.

So,
`0.427716*100\% = 42.7716 \%`

Thus, 42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.