Correlation and Application of Statistics to Problems 0/ Heredity 39 



And if from all our information t 



12 x (2 x -25 + 3 x -08 + 1 x '05 + '12) = 10-92 light-eyed. / 



Thus the best prediction gives 11 out of 12 children light-eyed. Actually 

 all 12 were light-eyed. Take again another family 2 parents hazel, 2 grand- 

 parents light, 1 hazel and 1 dark. Total family, 7 children. The prediction 

 is 7 (2 x -16-1- 2 x -08 + 1 x "05 + -12) = 4"55 light-eyed, the observed number 

 was 4. Of course Galton only claims to give the average family, and some 

 of the results he gives from his Table of 78 individual families are not 

 good. But his Table III in which he deals with 16 groups of different 

 ancestries is, considering what appears to me the doubtful character of his 

 assumptions, really surprising. Out of 827, 629 were observed to be light- 

 eyed. Predicted from parents only 623 were light-eyed, and from parents 

 and grandparents 614. As a rule, however, III gives a better result than I; 

 for example, out of 183 children, all of whose parents and grandparents were 

 light-eyed (none hazel), 174 were observed to be light-eyed; here III pre- 

 dicts 172, and I only 161. 



Prediction Table for Eye Colour in Offspring. 



It is certainly remarkable that the predictions should be even as accurate 

 as they are — and they are indeed not perfect — considering the contradictory 

 assumptions on which they are based*. Perhaps in the first glow of finding 

 such an amount of accordance Galton was justified in writing: 



"A mere glance at Tables III and IV will show how surprisingly accurate the predictions 



are, and therefore how true the basis of the calculations must be My returns are insufficiently 



numerous and too subject to uncertainty of observation to make it worth while to submit them 



* In particular Galton's assumption that the correlations of the offspring with the individual 

 parent, grandparent, great grandparent, etc., form the series r, r 3 , r 3 , etc., is incompatible with 

 his multiple regression coefficients \, ^, ^ T , etc. Any such series causes all those coefficients ex- 

 cept the first or parental coefficient to vanish, and reduces the ancestral multiple regression to 

 a simple biparental inheritance. Thus the parental characters determine completely those of 

 the offspring, as in the well-known case of the Mendelian theory of gametic characters. 



