From the family lung function data in Appendix A create a data set containing only those families from Burbank and Long Beach (AREA = 1 or 3). The observations now belong to one of two AREA-defined groups.

(a) Assuming equal prior probabilities and costs, perform a discriminant function analysis for the fathers using FEV1 and FVC.

(b) Now choose prior probabilities based on the population of each of these two cities (at the time the study was conducted, the population of Burbank was 84,625 and that of Long Beach was 361,334), and assume the cost of Long Beach given Burbank is twice that of Burbank given Long Beach. Repeat the analysis of part

(a) with these assumptions. Compare and comment.