How to find regression to the mean with the mean, standard deviation, possible X figures?

Answers (1)

Regression towards the mean is a phenomenon, not quite a number. A mathematical definition for expressing its occurrence is as follows:
Let X1, X2 be random variables with identical marginal distributions with mean μ. In this formalization, the bivariate distribution of X1 and X2 is said to exhibit regression toward the mean if, for every number c > μ, we have

μ ≤ E[X2 | X1 = c] < c,
with the reverse inequalities holding for c < μ.

Meaning, given a first result X1 which is 'distant' from the mean, the second result would, on average, be more likely closer to the mean.

Standard deviation increases the range of fluctuation yet has no effect on codependency.

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