The proportion of the variability in weight that can be explained by it's relationship with height is: 16% (Option C)
What is the justification for the above?
It is to be noted that the Coefficient of determination of r is the square of r value.
Hence,
R² = 0.4²
= 0.16 or 16%
The proportion of the variability in weight is option (C) 16%.
Note that the easiest technique to quantify the proportion of variation in an analysis of variance is to divide the sum of squares between groups by the sum of squares total.
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Full Question:
Suppose the correlation between height and weight for adults is r = 0.40. What proportion (or percent) of the variability in weight can be explained by the relationship with height?
A. 40%
B. 36%
C. 16%
D. 60%
E. None of the above.
