📉 Regression to Mean

Observed ρ̂—
Regression slope b—
Top 10% avg (X₁)—
Top 10% avg (X₂)—
Regression amount—
Galton (1886)
If X₁, X₂ ~ BivNormal(0,1,ρ):
E[X₂ | X₁] = ρ · X₁
The regression is (1−ρ)·σ toward μ.
ρ = 1 → no regression. ρ = 0 → full regression.

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