= Galton's stature regression
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<Francis Galton>'s paper <Regression towards mediocrity in hereditary stature by Francis Galton> analyzes adult offspring heights against the average of their parents' adjusted heights. He multiplied female heights by $1.08$ before making that parental average. Table I contains 928 adult offspring from 205 parental pairs; the opening prose instead states 930. Its grouped readout is a <median>, and the explanation of Plate IX describes a smoothed offspring deviation about two-thirds of the parental deviation.<Regression towards mediocrity in hereditary stature by Francis Galton>[Printed pp. 247-248, Table I; pp. 261-262, explanation of Plate IX(a): adjusted heights, counts, grouped medians and 2:3 deviation ratio]{ref}
These were parent-offspring records, not repeat readings of an unchanged signal. The paper's group tendency does not say that every child must be closer to the population <mean>. Galton also reports uncertainty over whether some recorded heights included shoes, a concrete <measurement error> limitation.<Regression towards mediocrity in hereditary stature by Francis Galton>[Printed p. 252: shoes-on versus shoes-off uncertainty and the average two-thirds height-deviation claim]{ref} The $0.6$ <Pearson correlation coefficient> and all generated values above are our chosen model, not a reconstruction of his data.
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