Regression to the mean
Will the top performers stay on top?
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What is the selected group’s expected second score?
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How it works & assumptions
Generate X=50+15Z₁ and Y=50+15(rZ₁+√(1−r²)Z₂). Select the highest first scores. E(Y|selected X)=50+r(mean X−50).
200 synthetic paired scores. Selection uses only the first score. Regression does not mean every individual moves toward the mean.
References: Introduction to Data Science, Chapter 15: Introduction to Regression, section 15.4
Random runs are reproducible from their setup links. Replay keeps the same seed; New random run changes it. A sample run need not equal the theoretical average.