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Taleb has previously undermined the typical interpretation of correlation with regards to the informational value it carries, showing how the uncertainty is reduced in a non-linear fashion.

With regards to a graph showing the relationship between COVID death tolls at lockdown time and the daily deaths afterwards, where the 15% of explained variability ($R^2$) was being used to defend the contribution, he makes the following statement:

an R-squared of .15 means, if you look at it generously, that almost all the variance is for random reasons, something like ~98% (conventional) or (entropy) >99.9%

How can these exact numbers be explained?
Is it related to the sampling distribution of the R^2?

Why is this such an unorthodox interpretation of these statistics?

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    $\begingroup$ I would say that statement is in general wrong. He or she may have been talked about a specific case. $\endgroup$ – user209249 Apr 14 at 21:34
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    $\begingroup$ @Sören I would say it is a general statement. He has previously undermined the informational value of correlation from a mutual information lens (twitter.com/nntaleb/status/1135116646442590208 here, for instance), but I am not sure I follow the distinction, nor why it seems to be an unorthodox or uncommon approach to interpret these statistics. $\endgroup$ – Kuku Apr 14 at 21:40
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    $\begingroup$ $98\%?$ Why not $85\%?$ $\endgroup$ – Dave Apr 14 at 21:46
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    $\begingroup$ @Dave I assume it to be since the informational value of a statistic is different from the amount of explained variance in the sample. But the derivation of those numbers (which I assume are related to information theory) is the gist of my question, indeed. $\endgroup$ – Kuku Apr 14 at 21:48
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    $\begingroup$ I think it means that Taleb thought not enough people were paying attention to him, so he should say something else that made little sense but would get headlines. $\endgroup$ – Peter Flom Apr 15 at 12:02
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The statement is incorrect. If the $r$-value were 0.15 then $r^2$, i.e., the 'explained fraction' would be 0.0225, which would then leave 0.9775 unexplained. However, 0.15 is already $r^2$ which means that $r=\sqrt{0.15}\approx0.387$, such that the explained fraction is 15%, and unexplained 85%

Moreover, the plot does not appear to have been normalized for frequency of occurrence based on relative national population, so that the actual explained fraction is likely higher than 15%.

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  • $\begingroup$ That would give a possible explanation for the "conventional" percentage given: a small mishap. But the question remains for the information perspective on it, and where the 99% "entropy" number comes from. $\endgroup$ – Kuku Apr 17 at 21:20
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    $\begingroup$ @Kuku My ability to read minds stops at the first disruptive mistake in a calculation. Maybe from something like this, who knows? $\endgroup$ – Carl Apr 17 at 21:36

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