It may seem odd, but one of the ways biologists can tell how old a lobster is involves measuring the concentration of a pigment called neurolipofuscin in the eyestalk of a lobster. (We are not making this up!) The authors of the paper “Neurolipofuscin is a Measure of Age in Panulirusargus, the Caribbean Spiny Lobster, in Florida” (Biological Bulletin : 55–66) wondered if it was sufficient to measure the pigment in just one eye stalk, which would be the case if there is a strong relationship between the concentration in the right and left eyestalks. Pigment concentration (as a percentage of tissue sample) was measured in both eyestalks for 39 lobsters, resulting is the following summary quantities (based on data read from a graph that appeared in the paper):
An alternative formula for computing the correlation coefficient that is based on raw data and is algebraically equivalent to the one given in the text is
Use this formula to compute the value of the correlation coefficient, and interpret this value.
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