Galton’s regression to and away from the mean

Author(s): Dennis de Champeaux*

Francis Galton’s achievements include the phenomenon of IQ regression to the mean of descendants in a hereditary context. A naïve interpretation yields that subsequent generations ultimately converge to the mean of the distribution, a fix point. We provide a simple assumption regarding descendants so that we obtain a counter balancing force, regression away from the mean, which will preserve an initial distribution. The argument is supported by ‘experimental’ statistics. We discretize a normal distribution, and subsequently replace many times a parent by a child, where a parent and a child are generated randomly, while the child is constrained by the regression equation. Our simple assumption guarantees that the original distribution is preserved. We obtain the regression to the mean effect from the perspective of the parent and a regression away from the mean effect from the perspective of the descendants. Our assumption, and others, corresponds, we believe, with a conjecture about the ‘Mechanics’ for the generation of a specific heritable trait.

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