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I'll get back to this. What I wanted, I just wanted to give you a graphic illustration, of what exactly does this Bayes estimator do? So, here, what I've done, is I've gone back and I've computed the old price sensitivities just using the least squares models, these open diamonds. So the idea is that there is going to be 83 diamonds out there, because I've got 83 stores. What this diamond is going to do, is it's going to tell me that the old price sensitivity is a -60 in one store and it's -125 in another store. 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 things and what this stuff is down at the bottom, I want to think about this related back to the demographic space. So, I've got to go back and say, look, with the demographics I haven't done anything with the least squares models, I haven't done anything with the demographics. So, what I'd like to do is just try to see in the data, is there any relationship I can observe. You know, I know that these least square estimates may have a lot of error. I'm not illustrating that the standard error is anyway. So the point is that can I go back and just look at the data and see that there's this relationship. So what I'm doing here is I go back and plot it against this Bayes prediction which is essentially a score of the demographic space. So what I'm going to do is, its this linear function of the demographics and essentially when I go back and do my Bayes model I think about, well, what would be the prediction of the Bayes models? And the point is, is that if you start looking at this stuff, you know you do see this linear relationship here - there is this positive relationship, is this, you move out this demographic space, you're increasing or your decreasing your own xxxxx sensitivity, since this is getting closer to zero. So this is my score, 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, you know, 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. So now the point is, is that let's go back and think about overlaying one of the Bayes predictions. So, here what I do is I recompute this stuff, and I come up with "what are my Bayes predictions"; so these are just the posterior means for each of these individual store parameters.
The point is, that, your pulling the least squared estimates towards this demographic, this prediction line.
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Yes?