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?

Question

Mathematics

Damien Barr

10 September, 03:07

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?

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Johnny Wilkerson · Answer 1

A correlation coefficient of + 1 or - 1 will indicate a direct linear model is the most appropriate but 0.94 shows that a very good direct correlation exists between the length of an aspen leaf and its surface area.

Step-by-step explanation:

this is because a values of r lying between + 1 and - 1, where + 1 indicates perfect direct correlation,-1 indicates perfect inverse correlation and 0 indicates that no correlation exists.

Between these values, the smaller the value of r, the less is the amount of correlation which exists. Generally, values of r in the ranges 0.7 to 1 and - 0.7 to - 1 show that a fair amount of correlation exists.

A correlation coefficient of 0.94 shows that a very good direct correlation exists between the length of an aspen leaf and its surface area but not necessarily indicate a linear model is the appropriate.