Consider the Diabetes dataset (posted with assignment).

Assume the population prior probabilities are estimated using the relative frequencies of the classes in the data.

(a) Produce pairwise scatterplots for all five variables, with different symbols or colors representing the three different classes. Do you see any evidence that the classes may have difference covariance matrices? That they may not be multivariate normal?

(b) Apply linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA). How does the performance of QDA compare to that of LDA in this case?

(c) Suppose an individual has (glucose test/intolerence = 68, insulin test =122, SSPG = 544. Relative weight = 1.86, fasting plasma glucose = 184). To which class does LDA assign this individual? To which class does QDA

relwt glufast glutest instest sspg group 1 0.81 80 356 124 55 Normal 2 0.95 97 289 117 76 Normal 3 0.94 105 319 143 105 Normal 4 1.04 90 356 199 108 Normal 5 1.00 90 323 240 143 Normal 6 0.76 86 381 157 165 Normal