regression to the mean. What's the formula?

Question

Mathematics

I came across this paragraph on the Internet:

The R2 value here is 0.609 which is ok but not great. The % regression to the mean is calculated as follows
% regression to the mean = 100% x (1 - R) = 1 - (0.608)1/2 = 100 x (1 - 0.779) = 22.1%

Just something in the vastness of Runet I can’t find a clear explanation of what it really is.
1. Am I right if I call it regression to the mean?
2. How did the author get 0.779?
3. How R2 is calculated and why R2 is used in the formula instead
of R2

Answer 1

R² is the so-called coefficient of determination. How does he work?
The initial variance of the variable y will be D1.
We set up a model - the variance of the D2 model, which, presumably, is less than D1 (especially if the entire sample is training, without examination; hello, retraining!).
Then R² = 1 − D2/D1 = (D1 − D2) / D1.
Dispersion is known to be measured in square parrots. And, moreover, for independent quantities D(x+y) = Dx+Dy. Thus, √(D1 − D2) ~ √R² is the spread that we explained by the model.
But he appears to be pulling an owl onto a globe. In his model, the explained scatter is 0.780 (it also can’t round), the unexplained scatter is √D2 ~ √(1 − R²) = 0.626, and depending on what you want to prove, you can manipulate the statistics in one direction or another. This is how I can say that with such spreads, only 0.780 / (0.780 + 0.626) = 55% skill, and 45% luck. So no, coefficient of determination, period. I repeat, for independent values, one spread is partially compensated by another, and D(x+y) = Dx+Dy. In square parrots.