(a) Comment on the pattern of correlation within the centrarchid family x1 throu

Question

(a) Comment on the pattern of correlation within the centrarchid family x1 through x4. Does the walleye appear to group with the other fish?

1. 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 T2 = Black crappie x3 = Smallmouth bass x1 = Bluegill r4 Largemouth bass x5 -Walleye 16 = Northern pike The estimated correlation matrix 0.4919 0.2635 0.3127 0.4653 0.3506 0.4108 0.4919 0.2635 0.4653-0.2277 0.0652 0.3127 0.3506-0.1917 0.2045 0.4108 0.0647 0.2493 0.2249 0.2293 0.2144 0.2277 -0.1917 0.0647 -0.2249 0.0652 0.2045 0.2493 0.2293-0.2144 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.

Explanation / Answer

Let us consider from x1 to x5

Among the centrarchid family ie x1 to x4

We see 0.4919 is the highest value ie X1 and X2 or Bluegill and Black crappie have the highest corelation

Th second highest correlation is 0.4653 between X1 and X4 or Bluegill and Largemouth bass

All other types of fish in the family have relatively low correlation compared to the above 2 sets

Higher the corelation means that the fishes must be difficult to catch as they get along well this can be known from the corelation matrix

Walleye or X5 has negative correlation with all the other fishes except X3 or the smallmouth bass which has almost zero corellation

The negative corelation means that catching the Walleye was relatively easy as it does not get along with other fishes

This could be one of the reasons as to why it is popular to catch the fish and hence most popular fish to eat

X1 X2 X3 X4 X5 X1 1 0.4919 0.2635 0.4653 -0.2277 X2 0.4919 1 0.3127 0.3506 -0.1917 X3 0.2635 0.3127 1 0.4108 0.0647 X4 0.4653 0.3506 0.4108 1 -0.2249 X5 -0.2277 -0.1917 0.0647 -0.2249 1

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