Annual financial data are collected for bankrupt firms approximately 2 years prior to their bankruptcy and for financially sound firms at about the...

Annual financial data are collected for bankrupt firms approximately 2 years prior to their bankruptcyand for financially sound firms at about the same time. The data on four variables X1= CF/TD = (cashflow)/ (total debt), X2 = NI /TA = (net income)/ (total assets), X3 = CA/ CL = (current assets)/ (currentliabilities), and X4 = CA/NS = (current assets)/ (net sales), are given in Table 11.4.a. Using a different symbol for each group, plot the data for the pairs of observations (x1,x2), (x1,x3)and (x1,x4). Does it appear as if the data are approximately bivariate normal for any of these pairsof variables?b. Using the n1= 21 pairs of observations (x1, x2) for bankrupt firms and the n2 =25 pairs ofobservations (x1,x2) for nonbankrupt firms, calculate the sample mean vectors 1 2 x and x and thesample covariance matrices S1 and S2.c. Using the results in (b) and assuming that both random samples are from bivariate normalpopulations, construct the classification rule (11-29) withp1 = p2 and c(1|2)= c(2|1).d. Evaluate the performance of the classification rule developed in (c) by computing the apparenterror rate (APER) from (11-34) and the estimated expected actual error rate E(AER) from (11-36).e. Repeat parts c and d, assuming that p1 = 0.05 and p2 = 0.95, and c(1|2)= c(2|1).Is this choice ofprior probabilities reasonable? Explain.f. Using the results in (b), form the pooled covariance matrix Spooled , and construct Fisher’s samplelinear discriminant function in (11-19). Use this function to classify the sample observations andevaluate the APER. Is Fisher’s linear discriminant function a sensible choice for a classifier in thiscase? Explain.