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It's a little more difficult to tell a good story about the priors. It really shows the need to develop some more theories about what is driving substitution between brands. What I've done here is think about 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? When we go back and think about this in terms of the r-squared, it's around 44 percent, so now let's carry it through and take a look at what the importance of the demographics is on all of our different coefficients. The one that I 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 is in terms of this r-squared value, so what I've just gone through is the fit is around 40 percent or 44 percent for the premiums.
Let's think about some of the other effects. 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, and they become important for the feature price terms. Now, it's also important to think about the impact of the prior. What's the importance of the prior on the effect of the prediction relationship? You see here that as my prior increases these demographics are becoming more important. Which makes sense -- the variance is decreasing, the predicted values are still there, so you know that it's making this ratio bigger.
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