In a recent paper (Management Science, Vol. 19, No. 11, pp. 1213-1221) Morrison presents an interesting and useful explanation relating to empirical studies in market segmentation and their marked failure in explaining much of the variance in individual purchasing behavior. The explanation centers around the fact that, while a model may be very effective in predicting the average number of purchases for a particular individual, it may be very poor in predicting the exact number of purchases for that individual during a specified time period. He proceeds to show that, under a given set of assumptions, the upper limit of the population R 2 statistic for the models used in most empirical studies in this area is considerably less than 1.0. He further states that, in cases where the model explains less than 50% of the variance of the expected number of purchases for individuals, R 2 (true population value) becomes negative. This conclusion is one which lacks intuitive appeal and deserves further consideration.
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