To illustrate the fit of the model, Exhibit 1 shows both the observed and predicted results for two measures for the ten leading brands of cereals and petrol - namely the average purchase frequency of each of the ten and the percentage of its buyers who are 100%-loyal. There were fractionally more 100%-loyal buyers than predicted for petrol, but the figures are very low either way and clearly show Double Jeopardy trends for the smaller brands. And yes, All Bran (the 7th cereal) seems a bit of a `niche' brand (ie apparently heavily bought by its relatively few buyers, although the real explanation is that only some cereal buyers are in the market for this type of product).