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I'll get back to this. I just wanted to give you a graphic illustrationof what exactly this Bayes estimator does? So what I've done is I've computed the old price sensitivities just using the least-squares models, these open diamonds. The idea is that there are going to be 83 diamonds out there, because I've got 83 stores. This diamond is going to to tell me that the old price sensitivity is a -60 in one store and it's -125 in another store. For these old prices, since this is the sub R model, you've got to multiply it times price (prices per ounce), and if you multiply this stuff in terms of the price elasticity, it's going to come down to between -5 and 0, somewhere in there, probably -2. Okay, so now I've done all this and I want to think about this as it is related to the demographic space. What I'd like to do is just try to see if there is any relationship I can observe in the data. I know that these least square estimates may have a lot of error. I'm not illustrating what the standard error is anyway. The point is whether I can just look at the data and see that there's this relationship. So I plot it against this Bayes prediction which is essentially a score of the demographic space. It's this linear function of the demographics and essentially when I do my Bayes model I think about, well, what would be the prediction of the Bayes models? The point is that if you start looking at this stuff, you do see this linear relationship here -- there is this positive relationship, as you move out this demographic space. This is my store, the dashed line is the pooled models, and the point is that, since I didn't put an informative prior on this and I'm letting the data drive it, this line could have had any relationship. It could have been negative, it could have been very positive, or it could have been flat and I could have gotten something a little more like the pooled model. Now let's think about overlaying one of the Bayes predictions. Here what I do is I recompute this stuff, and I come up with my Bayes predictions, so these are just the posterior means for each of these individual store parameters.
The point is that you're pulling the least-squared estimates towards this demographic, this prediction line.
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Yes?