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Douglas_Knight comments on The Mathematics of Beauty [link] - Less Wrong Discussion
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Comments (5)
Covariance is one keyword. If the data is linear but not maximal dimensional, then you get covariance. This is to be expected in situations like this, where you convert a scale to a bunch of booleans. ETA: and even if one did not expect adjacent values to be correlated, that the total number of ratings is about the same is a reduction of dimension.
But if the data is not linear, many more things can go wrong. I don't know names for them.
Matt Simpson: I suppose that could solve the problem of covariance, but that's not what I'm talking about.
It would be interesting to see higher-dimensional plots. For example, the scatter plot of average-score vs the number of messages could be colored according to the number of ratings of 1. And similar charts for other ratings.
That is a good example of an error that one could make from believing the data is linear (and thus trusting the regression coefficients) when it is not linear. If their non-linear model were correct, we would get regression coefficients like what we see. If we trusted the regression coefficients too much (implicitly assuming the data is linear), then the positive coefficient on the number of 1s would suggest that having all 1s is good. But it is not. Their model says it is not and the data says it is not (eg, the scatter plot).
I think that is what you are saying. It is certainly not their mistake - they believe their model. I am not saying anything so specific, but it is the type of mistake that I am talking about. Also, there are lots of non-linear models that lead to the same regression.