Question

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 model.


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.

Answer 1

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

Explanation:

The correlation Coefficient of 0.94 obtained is peculiar to the linear model upon which the data was represented. Since the correlation Coefficient usually span between - 1 to + 1, it is very possible that, if the dataset is represented on a different model such as an exponential or quadratic model, the correlation percentage obtained may be better than that produced by the linear model.