Question

Suppose the correlation between height and weight for adults is +0.40. What proportion (or percent) of the variability in weight can be explained by the relationship with height

Answer 1

Answer:

We are given the correlation between height and weight for adults is 0.40.

We need to find the proportion of the variability in weight that can be explained by the relationship with height.

We know that coefficient of determination or R-square measures the proportion or percent of variability in dependent variable that can be explained by the relationship with independent  variable. There the coefficient of determination is given below:

$R^{2}=r^{2}=0.40^{2}=0.16$

Therefore, the 0.16 or 16% of the variability in weight can be explained by the relationship with height