Customer Relationship Management: A Database Approach MARK 7397 Spring 2007 Customer Relationship Management: A Database Approach Class 11 Discriminate Analysis Werner Reinartz James D. Hess C.T. Bauer Professor of Marketing Science 375H Melcher Hall jhess@uh.edu 713 743-4175

Discriminant Analysis of Toaster Customers Size of GS = location of Goldstar buyer Family BD = location of Black & Decker buyer 10 9 BD BD 8 GS 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1 Taste for 10 20 30 40 50 60 70 80 90 100 Speed

Means and Confidence Circles Toaster Customers Means and Confidence Circles Size of Family Location of average Black & Decker buyer 10 9 BD BD 8 GS Location of average Goldstar buyer 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1 Taste for 10 20 30 40 50 60 70 80 90 100 Speed

Means and Confidence Ellipses Toaster Customers Means and Confidence Ellipses Size of Family 10 9 BD BD 8 GS 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1 Taste for 10 20 30 40 50 60 70 80 90 100 Speed

Discriminant Analysis of Toaster Customers Size of Family 10 9 BD BD 0=-2.0-.013TS+.456SF or SF=4.2+.03TS 8 GS 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1 Taste for 10 20 30 40 50 60 70 80 90 100 Speed

Assignment of Observation to Population Suppose we have computed discriminant coefficients b and have observed a value X for an observation. Suppose that a priori we think the two populations have probabilities qBD and qGS and the costs of misclassification are C(BD|GS) and C(GS|BD). Let the group centroids be XBD and XGS then the observation should be allocated to GS if Xb < -------------- + ln --------------------- XBDb+XGSb qBDC(GS|BD) qGSC(BD|GS) 2 Note: if prior probabilities and costs are symmetric then the last term above is ln(1)=0. However, suppose that qGS=2/3 and misclassifying a GS as BD is 5 times more costly than misclassifying a BD as GS. Then the threshold for allocating to GS is easy since ln(10)=+2.3.