Annual financial data are collected for bankrupt firms approximately 2 years prior to their bankruptcy
and for financially sound firms at about the same time. The data on four variables X1= CF/TD = (cash
flow)/ (total debt), X2 = NI /TA = (net income)/ (total assets), X3 = CA/ CL = (current assets)/ (current
liabilities), 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 pairs
of variables?
b. Using the n1= 21 pairs of observations (x1, x2) for bankrupt firms and the n2 =25 pairs of
observations (x1,x2) for nonbankrupt firms, calculate the sample mean vectors 1 2 x and x and the
sample covariance matrices S1 and S2.
c. Using the results in (b) and assuming that both random samples are from bivariate normal
populations, construct the classification rule (11-29) with
p1 = p2 and c(1|2)= c(2|1).
d. Evaluate the performance of the classification rule developed in (c) by computing the apparent
error 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 of
prior probabilities reasonable? Explain.
f. Using the results in (b), form the pooled covariance matrix Spooled , and construct Fisherâs sample
linear discriminant function in (11-19). Use this function to classify the sample observations and
evaluate the APER. Is Fisherâs linear discriminant function a sensible choice for a classifier in this
case? Explain.
