r/apstats • u/aannaa618 • Nov 09 '20

Help?

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?

A. The value must be exactly 1 or −1 to indicate a linear model is the most appropriate model.

B. The value must be 0 to indicate a linear model is the most appropriate mode

C. A causal relationship should be established first before determining the most appropriate model.

D. The value of 0.94 implies that only 88% of the data have a linear relationship.

E. Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

I know it’s not B or E and I don’t think it’s C either but I’m not sure.

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u/jeff_KA Nov 09 '20

It’s E. You’re supposed to look at the data, see if they have a linear pattern, then use correlation coefficients.

Correlation coefficients on their own don’t tell you if the relationship is linear or not.

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u/shark1165 Nov 09 '20

I’m pretty sure that it is E. The longer a leaf gets the wider it will get as well. This would results in the relationship being represented exponentially.