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?

a) 26%
b) 69.49%
c) 51.8%
d) 45.29%

Answer 1

The percent of variation in the minutes doing homework that is not explained by the number of hours a child plays video games is approximately 45.24%, which corresponds to answer choice d.

Step-by-step explanation:

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.

To find the percent of variation in the minutes doing homework that cannot be explained by the number of hours a child plays video games, we use the coefficient of determination, which is r². The coefficient of determination is calculated by squaring the correlation coefficient:

r² = (-0.74)² = 0.5476.

This value represents the percent of variation in y that can be explained by variation in x using the regression line. To find the percent that cannot be explained, we subtract this value from 1:

1 - r² = 1 - 0.5476 = 0.4524.

Expressed as a percentage, this is approximately 45.24%, which is answer choice d.