FILIAL REGRESSION 319 



" To put the same conclusion in another form, the most pro- 

 bable value of the deviation from P, of his mid-ancestors in 

 any remote generation, is zero " (p. 105). 



Pearson interprets Filial Regression in similar terms. " A 

 man is not only the product of his father, but of all his past 

 ancestry, and unless very careful selection has taken place 

 the mean of that ancestry is probably not far from that of the 

 general population. In the tenth generation a man has [theo- 

 retically] 1024 tenth great-grandparents. He is eventually 

 the product of a population of this size, and their mean can 

 hardly differ from that of the general population. It is the 

 heavy weight of this mediocre ancestry which causes the son of 

 an exceptional father to regress towards the general population 

 mean ; it is the balance of this sturdy commonplaceness which 

 enables the son of a degenerate father to escape the whole burden 

 of the parental ill. Among mankind we trust largely for our 

 exceptional men to extreme variations occurring among the 

 commonplace, but if we could remove the drag of the mediocre 

 element in ancestry, were it only for a few generations, we 

 should sensibly eliminate regression or create a stock of excep- 

 tional men. This is precisely what is done by the breeder in 

 selecting and isolating a stock until it is established." {Grammar 

 of Science, 1900, p. 456.) 



Prediction. — When we know the heights of a thousand fathers 

 of a given stock, and the heights of their sons, and the mean 

 height of the general population, we have a basis for constructing 

 a " regression equation," which may be used to calculate the 

 probable stature of the son of any father. But this prediction 

 may be wide of the mark, since exceptional individual variability 

 often occurs. What will not be wide of the mark, however, is a 

 prediction as to the average height of the sons of a group of, say, 

 fifty fathers. If the formula [stature of son = 38""45 + "446 

 X stature of father] be applied to fifty English middle-class 

 fathers of the same height, it will be found that their sons have 



