5.11 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 Panulirus argus, the Caribbean Spiny Lobster, in Florida” (Biological Bulletin [2007]: 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 in the following summary quantities (based on data read from a graph that appeared in the paper):

n 5 39 ox 5 88.8 oy 5 86.1 oxy 5 281.1 ox2 5 288.0 oy2 5 286.6 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 r 5 oxy 2 soxdsoyd n Îox2 2 soxd2 n

Îoy2 2 soyd2 n

Use this formula to compute the value of the correlation coefficient, and interpret this value.