Question

The correlation coefficient r between the number of hours a child plays video games, x, and the number of minutes spent doing homework each day, y, is - 0.74.

What percent of the variation in the number of minutes doing homework cannot be explained by differences in the children's ages?

Answer 1

45.24%

Explanation:

Given that:

Correlation Coefficient (r) between number of hours a child play video games and number of minutes spent doing homework = - 0.74

The Coefficient of determination (r²) gives the percentage of variation in the dependent variable which can be explained by the independent variable.

Hence, the r² value = (-0.74)² = 0.5476 ; 54.76% which is about 55% variation in the number of minutes spent doing homework can be explained by the number of hours a child plays video games.

Hence the unexplained variance due to differences in children's ages is (100% - 54.76%) = 45.24%