Over a period of five years in the 1990s, yearly samples of fishermen on 28 lakes in Wisconsin were asked to report the time they spent fishing and how many of each type of game fish they caught. Their responses were then converted to a catch rate per hour for
The estimated correlation matrix (courtesy of Jodi Barnet)
is based on a sample of about 120. (There were a few missing values.)
Fish caught by the same fisherman live alongside of each other, so the data should provide some evidence on how the fish group. The first four fish belong to the centrarchids, the most plentiful family. The walleye is the most popular fish to eat.
(a) Comment on the pattern of correlation within the centrarchid family XI through X4. Does the walleye appear to group with the other fish?
(b) Perform a principal component analysis using only X1 through X4. Interpret your results.
(c) Perform a principal component analysis using all six variables. Interpret your results.