Why was the symbol $r$ chosen to denote Pearson's product moment correlation?

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    $\begingroup$ The question has been motivated by a comment of @IsabellaGhement in this thread. Hint: there is a paper by Karl Pearson called "Notes on the History of Correlation" (1920). Perhaps it contains an answer? $\endgroup$ – Richard Hardy Sep 22 '18 at 19:56
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    $\begingroup$ The population correlation is often denoted $\rho$ so using $r$ for the sample correlation maintains an alphabetical parallel (link). This probably doesn't fully answer your question so I'll just leave this as a comment. $\endgroup$ – SecretAgentMan Sep 22 '18 at 19:58
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    $\begingroup$ I'm still curious to see a good answer to this question...after my weak comment, your question still remains. I have half a mind to delete my comment and wait for a good answer. $\endgroup$ – SecretAgentMan Sep 22 '18 at 20:06
  • $\begingroup$ Then the question may reduce to why $\rho$ is used for population correlation. Maybe a simple as observing that correlations are defined as ratios. $\endgroup$ – BruceET Sep 22 '18 at 21:08

From Pearson's "Notes on the history of correlation"

The title of Galton's R. I. lecture was Typical Laws of Heredity in Man. Here for the first time appears a numerical measure $r$ of what is termed 'reversion' and which Galton later termed 'regression'. This $r$ is the source of our symbol for the correlation coefficient.

This 1977 lecture was also printed in Nature and in the Proceedings of the Royal Institution

From page 532 in Francis Galton 1877 Typical laws of heredity. Nature vol 15 (via galton.org)

Reversion is expressed by a fractional coefficient of the deviation, which we will write $r$. In the "reverted" parentages (a phrase whose meaning and object have already been explained) $$y = \frac{1}{r c \sqrt{\pi}} \cdot e ^{- \frac{x^2}{r^2c^2}}$$ In short, the population, of which each unit is a reverted parentage, follows the law of deviation, and has modulus, which we will write $c_2$, equal to $r c_1$.


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