2. Baten, Tack, and Baeder (1958) compared judges' scores on fish pre- pared by three methods. Twelve fish were cooked by each method, and several judges tasted fish samples and rated each on four vari- ables: aroma, flavor, texture, and moisture. The data can be found in the data set fish.csv. (a) Carry out tests of significance for the discriminant functions and find the relative importance of each as in where A; are the eigenvalues. Do these two procedures agree as to the number of important discriminant functions? (b) For the important discriminant functions (see your answer in part (a)), find the correlation between your 2's and the independent variables. c)Comment on the contribution of the variables to separation of groups. d)Can you construct an interpretation of z1? e) Plot the two discriminant functions for each observation. 1. Four measurements were made on two species of flea beetles. The variables were Y = distance of transverse groove from posterior border of prothorax (um) Y2 = length of elytra (in 0.01 mm) = length of second antennal joint (in m) 34 = length of third antennal joint (in m) The data can be found in the data set beetles.csv. (a) Find the discriminant function coefficient vector, a. (b) Calculate t-tests for individual variables. This would involve us- ing t.test in R. or proc ttest in SAS. (c) Calculate the correlation between the discriminant function, 21, and each of the independent variables x1, x2, 23, 24. (d) Compare the results of (b) and (c) as to the contribution of each variable to separation of the groups. (e) Can you come up with an interpretation of 21?