Francis Galton, answered from the texts and cited to the page.
When I set out to study inheritance I found the naturalists' method — the tracing of single pedigrees — too coarse to yield a law, and I turned to the mathematics of the average and the deviation. I found that human stature, and every faculty I could measure, distributes itself about a mean according to the same law of error that governs the errors of astronomers; that this distribution is astonishingly stable from one generation to the next; and, most unexpectedly, that the children of exceptional parents are on the average less exceptional than their parents — they regress toward the general mean.12
I gave this regression a measure, drew the line that predicts the child's stature from the parents', and saw in it the first glimpse of what I called co-relation: the degree to which two variable things are yoked together, so that knowing one you may partly predict the other. Here was the true instrument for the study of heredity and of much else — a way of stating the strength of a tie between any two measurable characters without pretending to a certainty the data do not hold. Whenever you can, count; and when you have counted, find the law of the scatter.345
Most obviously A B does not agree with C D; therefore Sons do not, on the average, resemble their Mid- Parents. On examining these lines more closely, it will be observed that A B cuts C D at a point M that fairly corresponds to the value of 68|- inches, whether its value be read on the scale at the top or on that at the side. This is the value of P, the Mid-Stature of the population.Natural Inheritance, pp. 97–98
The one tendency is to deviate from P as much as his brother, and the other tendency is not to deviate at all. The result is a compromise. As the average Eegression from either Parent to the Son is twice as great as that from a man to his Brother, a man is, generally speaking, only half as nearly related to either of his Parents as lie is to his Brother.Natural Inheritance, pp. 110–111
Sections of surface of frequency parallel to XY are true ellipses. (Obs. — Apparently true ellipses.) MX: YO = 6: 17 '5, or nearly 1: 3. (Obs.— 1: 3.) Major axes to minor axes = J 7: ^ 2 = 10: 5*35. (Obs.— 10: 5-1.) Inclination of major axes to OX = 26° 36". (Obs. 25°.) Section of surface parallel to XZ is a true Curve of Frequency. (Obs. — Apparently so.) " Prob. Error the Q of that curve, = 1.07 inch.Natural Inheritance, pp. 104–105
It must be clearly understood that there is nothing in these statements to invalidate the general doctrine that the children of a gifted pair are much more likely to be gifted than the children of a mediocre pair. They merely express the fact that the ablest of all the children of a few gifted pairs is not likely to be as gifted as the ablest of all the children of a very great many mediocre pairs.Natural Inheritance, pp. 106–108
Then the number of entries in each square inch were counted, and copied in the form in which they appear in the Table. I found it hard at first to catch the full significance of the entries, though I soon discovered curious and apparently very interesting relations between them.Natural Inheritance, pp. 101–102
This is Galton's most secure and least contested legacy. Regression toward the mean and the concept of correlation, formalized by Karl Pearson into the correlation coefficient, founded modern mathematical statistics, biometry, and psychometrics, and are used universally across the sciences. The one substantive correction is conceptual: Galton at first half-read regression as a biological tendency of offspring to revert toward a racial type, whereas it is a general mathematical consequence of imperfect correlation between any two variables — nothing biological is required. With that understood, the machinery is simply correct and remains in daily use; the agent stands on the firmest ground here.