If Galton did not use least squares then how was he drawing his regression slopes? I read the following from a document online here.

Galton was full of
ideas but was no
mathematician. He
didn’t even use least
squares, preferring to
avoid unpleasant
computations.

If Galton did not use least squares then how was he drawing his regression slopes?


The way Galton proceeded to his regression estimate can be found in Stephen Stigler's book, The History of Statistics, as well as a 1997 paper of his, Regression towards the mean, published in Statistical Methods in Medical Research. The above table is reproduced from that paper.
The table was used by Galton to decompose the variability of the second generation $d$ as $d^2=v^2+r^2c^2$ where $c$ is the variability of the first generation and $v$ the dispersion of the offspring, since

the position of a second generation individual was the sum of its `reverted' averaged displacement from its parent (say $rz$, where $z$ was the first generation position) and its random deviation from that position (p.110)

and conclude from the stability over generations that $d=c$. The core of Galton's derivation "with a slight assist from the Cambridge mathematician JH Dickson", is to express the data in the curve as a discretised observation of a bivariate Normal and derive the conditional expectation of the height of the adult children on the height of the mid-parent. (Which in itself was an amazing feat for the time.)
