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The priors.. it's a little more difficult to tell a good story about them, at least in the xxx. It goes back to thinking about, well, it really shows the need to develop some more theories about, you know, what is it thats driving substitution between brands. Now, what I've done here, is, let's go back and think about, well, what's the effect, the fit between the demographics. How important is the demographics? When I put this line up, what the line was saying is how disperse are the Bayes estimates around the predicted values? So in this case, when we go back and look at the values, the r-squared, if you to think about this in r-squared, it's around 44 percent, so now lets go through and carry it through and take a look at what the importance of the demographics on all of our different coefficients? So the one that I have just went through was the effects of the old price on the national, so here you see that the top is in terms of standard deviation, the bottom was in terms of, like this r-squared value, so what I've just went through is here the fit is around 40 percent or 44 percent for the premiums.
So now lets go back and think about some of the other effects. So, what's happening in terms of the r-squared, you'll notice that these demographic variables are important for our price terms, they become less important for the cross-price terms, they become important for the feature price terms. Now, what's also important is to think about, well, what's the impact of the prior? xxxxxx What's the importance of the prior on the effect of prediction relationship? So what you see here, is that as my prior increases these demographics are becoming more important. Which is making sense, you know, the variance is decreasing, the predicted values are still there, so you know that its changing this ratio, it's making it bigger.