-Sophia was impressed, but had some cutting methodological critiques. The paper had given [residual](https://en.wikipedia.org/wiki/Errors_and_residuals) statistics of each facet against the other—like the mean and standard deviation of Enthusiasm _minus_ Assertiveness—so I assumed you could randomly generate one facet, and then use the residual stats to get a "diff" from one to the other. Sophia pointed out that you can't actually use residuals for sampling like that, because the actual distribution of the residual was highly dependent on the first facet. Given an unusually high value for one facet, taking the overall residual stats as independent would imply that the other facet was equally likely to be higher or lower, which was absurd. Sophia built her own model in Excel using the correlation matrix from the paper, and found a classifier with 68% accuracy.
+Sophia was impressed, but had some cutting methodological critiques. The paper had given [residual](https://en.wikipedia.org/wiki/Errors_and_residuals) statistics of each facet against the other—like the mean and standard deviation of Enthusiasm _minus_ Assertiveness—so I assumed you could randomly generate one facet, and then use the residual stats to get a "diff" from one to the other. Sophia pointed out that you can't actually use residuals for sampling like that, because the actual distribution of the residual was highly dependent on the first facet. Given an unusually high value for one facet, taking the overall residual stats as independent would imply that the other facet was equally likely to be higher or lower, which was absurd.
+
+(For example, suppose that "height" and "weight" are correlated aspect of a Bigness factor. Given that someone's weight is +2σ—two standard deviations heavier than the mean—it's not plausible that their height is equally likely to be +1.5σ and +2.5σ, because the former height is more than seven times more common than the latter; the second facet should [regress towards the mean](https://en.wikipedia.org/wiki/Regression_toward_the_mean).)
+
+Sophia built her own model in Excel using the correlation matrix from the paper, and found a classifier with 68% accuracy.