# Informational value of R squared and correlation? [closed]

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?

• I would say that statement is in general wrong. He or she may have been talked about a specific case.
– user209249
Apr 14, 2020 at 21:34
• @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.
– Kuku
Apr 14, 2020 at 21:40
• $98\%?$ Why not $85\%?$
– Dave
Apr 14, 2020 at 21:46
• @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.
– Kuku
Apr 14, 2020 at 21:48
• 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. Apr 15, 2020 at 12:02

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%