To determine the proportion of variability in weight that can be explained by the relationship with height, we need to use the squared value of the correlation coefficient, often denoted as [tex]\( r \)[/tex].
The given correlation coefficient [tex]\( r \)[/tex] is [tex]\( 40.40 \)[/tex]. This can be expressed as [tex]\( r = 0.4040 \)[/tex] in decimal form.
To find the proportion of variability explained by the correlation, follow these steps:
1. Square the correlation coefficient: This gives us the coefficient of determination [tex]\( r^2 \)[/tex].
[tex]\[
r^2 = (0.4040)^2
\][/tex]
2. Convert the result to a percentage: Because [tex]\( r^2 \)[/tex] represents the proportion of the variability, expressing it as a percentage involves multiplying by 100.
[tex]\[
\text{Proportion of variability explained} = r^2 \times 100
\][/tex]
Calculating this, we get:
[tex]\[
r^2 = (0.4040)^2 = 0.163216
\][/tex]
[tex]\[
\text{Proportion of variability explained} = 0.163216 \times 100 = 16.3216 \%
\][/tex]
As none of the given options account for the decimal portion exactly, we round to the nearest whole number, which is 16%.
Therefore, the correct answer is:
[tex]\[
\boxed{16 \%}
\][/tex]
