20 FRETS, ERFELIJKHEID, CORRELATIE EN REGRESSIE. 
cases in which the variability (standarddeviation) is equal for 
both contrasted characters, regression and correlation have the 
same value. This happened for instance in the material which 
served GALTON as a basis for his study on the inheritance of the 
length of the human body. | 
2. The coefficient of regression for mothers and daughters is 
in my material somewhat larger than for fathers and sons. That 
for mothers and daughters (0.32) differs little from the original 
coefficient of regression of GALTON (1/3). 
3. The coefficient of regression of grandparents and grandchil- 
dren shows for the possible combinations (tab. II) rather large 
‘ differences. For all grandparents and grandchildren the coefficient 
of correlation is 0.134. | 
4. The coefficient of regression for collateral heredity is in my 
material about 0.45. 
5. The values of the coefficients of regression that are found by 
me agree rather well with the values of the coefficients of regres- 
sion that are calculated by PEARSON for a theoretical population, 
in whichn pairs of factors have, alternative heredity (whilst the 
value of n is indifferent). | 
6. Regression is explained by GALTON by the conception of 
the stability of type and of heredity. 
JOHANNSEN and the workers on experimental heredity explain 
the regression by the simultaneous presence in a population of 
hereditary and non-hereditary variations, and by assuning that 
hereditary variations of an average value occur very often and 
those of an extreme value very rarely. 
In material with non-hereditary variations only, the regression 
is 0. (pure Line). In material in which all the different hereditary 
variations occur in equal numbers, — each with some non-here- 
ditary variations — the regression is 1. 
From PEARSON's „generalised theory of alternative heredity” it 
appears that the regression may be explained on the assumption 
of the presence of n hereditary factors. These cause the frequency 
of the different hereditary variations, while the mendelian heredity 
itself causes the stability of the population. This theory for the 
explanation of the regression needs no special conception of sta- 
bility of type. 
