66 
Variation and Correlation in Brain-Weight 
DiAGKAJi XIX. Probable Brain-weight for given Body-weight. 
Bavarian ? Total. 
( 
> 
< 
< 
1 
( 
> . 
< 
1 
( 
) 
1 
> 
< 
E) 
) 
( 
1 
~ 1350 
S 
[Si 
I 1200 
S 
Cq 1150 
17-5 22-5 27-5 32 5 37 5 42 5 47 5 52-5 57-5 62 5 67-5 72-5 77 5 82 5 875 
Body -weight [ = Wg) in kilograms. 
Through the great bulk of the observations the regression is evidently linear*. 
The male series comes very close to linearity. 
The equations to the regression lines may now be given. In addition to the 
equation showing the regression of brain-weight on body-weight I have included 
multiple regression equations giving the probable brain-weight for given types of 
body-weight and stature together. The significance of the letters is as follows : 
W denotes the probable brain-weight of an array having a mean body-weight in 
kilograms Wjg, or body-weight Wjj and stature S. 2 is the standard deviation of 
the array. 
(27) Bavarian ^ Tr= 1263 -308-1-1 -886 TF^, 2 = 118-439 
(28) „ ? ir= 1121 -6214- 2-265 I-F^, 2 = 103-495 
(29) „ ^ TF= 917-748 -1-2-234 ^-f 1-355 TFg, 2 = 117-711 
(30) „ $ Tr= 741 -078 + 2-646 »S'-H -593 IF^, 2 = 102-432 
The correlation of brain-weight with body-weight is of about the same degree 
as the correlation of the former with the stature, but the regression approaches 
more closely to linearity in the case of body-weight. As in the other cases the 
female shows the higher correlation. 
The absolute increase of brain-weight with every increase of 10 kilos, in body- 
weight is for the males 18-86 gr. and for the females 22-65 gr. Equations (29) and 
(30) show that in each case stature contributes absolutely more to an increase in 
brain-weight than does body-weight. The exact proportions are as follows : in 
order to bring about a change in brain-weight equal to that produced by an 
increase of stature of 10 cm. the body- weight would have to be increased 
16"5 kilos, in the males, and 16'6 kilos, in the females. The greater dependence of 
the brain-weight on bodily characters in the female as compared with the male is 
very well shown in equations (29) and (30). 
Of. pp. 61, 62. 
