To determine the proportion of the variation in head circumference that can be explained by the variation in height, we can use the correlation coefficient. The correlation coefficient, denoted as [tex]\( r \)[/tex], quantifies the strength and direction of the linear relationship between two variables.
Given:
- The correlation coefficient [tex]\( r \)[/tex] is 0.803.
The proportion of the variation that can be explained is found by squaring the correlation coefficient [tex]\( r \)[/tex]. This value, [tex]\( r^2 \)[/tex], is known as the coefficient of determination.
Let's walk through the steps:
1. Calculate the coefficient of determination ([tex]\( r^2 \)[/tex]):
[tex]\[
r^2 = (0.803)^2
\][/tex]
2. Compute the value:
[tex]\[
r^2 = 0.6448090000000001
\][/tex]
3. Round the computed value to one decimal place:
[tex]\[
\text{Rounded } r^2 = 0.6
\][/tex]
Thus, the proportion of the variation in head circumference that can be explained by the variation in height is 0.6, or 60% when expressed as a percentage.
