Question

the correlation coefficient $r$ between a childs age, $x$, and the number of minutes spent doing homework each day, $y$, is 0.694. what percent of the variation in the number of minutes doing homework cannot be explained by differences in the childrens ages?
69.4%
30.6%
51.8%
48.2%

Explanation:

Step1: Calculate coefficient of determination

The coefficient of determination $R^{2}=r^{2}$. Given $r = 0.694$, then $R^{2}=(0.694)^{2}=0.481636$.

Step2: Find unexplained variation

The proportion of unexplained variation is $1 - R^{2}$. So, $1-0.481636 = 0.518364$.

Step3: Convert to percentage

To convert to percentage, multiply by 100. $0.518364\times100 = 51.8364\%\approx51.8\%$.

Answer:

51.8%