Galton's stature regression

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.^[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.^[ref] The $0.6$ Pearson correlation coefficient and all generated values above are our chosen model, not a reconstruction of his data.