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Mathematics
Set Theory, Logic, Probability, Statistics
Is Newtonian Mechanics as Correct as General Relativity?
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[QUOTE="FallenApple, post: 6016302, member: 585259"] That makes sense. Another example in science is that Newtonian physics predicts well, but is wrong. But it is a limiting case of General Relativity, so the false theory of Newtonian Physics is still at least directly related to the truth. If certain medications work well the vast majority of the time, then it likely isn't a coincidence. Is the mathematical/statistical reason for setting the bar lower for "intuitive variables" is because even if by itself it isn't significant, it could be after including it? Because the error term for the model becomes correlated to the input of confounders? Because that error term wouldn't be irreducible. So that error the would be absorbing some of the influence? So the unintuitive factor has a higher bar because it is unlikely, given the theory is true, to be a confounder and adding it probably will just complicates things for interpretation because of the combinatorial issue you noted. Also, I think from a predictive standpoint, it would be pretty bad as well right? Because it increases the dimensionality of the input space and will result in higher variance of outcomes after validation. But wouldn't this result in a tradeoff? Because sometimes there are many confounders, so including them will be necessary for getting good explanation and better model fit(Lower RSS), but will increase of variance of the predicted outcome on a validation set if we were to obtain one. [/QUOTE]
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Is Newtonian Mechanics as Correct as General Relativity?
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