Raymond Pearl 
n 
Diagram XXIII. Probable Brain-weight for given Skull Breadth. 
Bohemian ? Young. 20 — 59 years. 
1450 
1400 
t 1350 
1300 
1250 
) 
< 
) 
( 
< 
) 
132-5 137-5 142-5 147 5 152 5 157-5 162 5 
iSkull Breadth ( = B) in millimetres. 
Thi^ough the bulk of the observations the regression is very evidently linear. 
Diagram XXI shows that the considerable deviations of rj from r and S^i/ from 
zero in the case of the male brain-weight and skull breadth regression are really 
due to the inclusion in the material of five individuals which are to be regarded 
as either erroneously measured or recorded, or else abnormal or extremely rare 
normal cases (cf Table 31, Appendix). 
The regression equations follow. In these equations W denotes the probable 
brain-weight in grams of an array of individuals having a mean skull length L 
and skull breadth B in millimetres. 
(31) Bohemian ^ T^^=8-589Z- 52-650, 2= 96-548 
(32) „ S TF=8-076-S + 253-596, 2 = 102-170 
(33) „ ? TF=6-215Z-|- 264-265, 2= 88-466 
(34) „ ? TF=8-646 5-t- 68-434, 2= 81-908 
(.35) „ $ H^=6-751Z-|- 5-082 5-489-649, 2= 99-745 
(.36) „ ? TF=4-696Z-|- 7-766 5 - 602-994, 2= 77-893 
One rather curious point may be noted here in passing. As the figures stand 
a smaller probable error will be made in estimating the mean brain-weight of 
males from a knowledge of skull length alone (equation 31) than if both length 
and breadth of skull are used. This apparent paradox arises for the following 
reason*. The standard deviation of the array in the regression of a\ on its 
associated variables x„ and is given by 
2 = vr 
/here 
rj + ?-j 
1 - r,3^ 
When the regression is of on Xn alone the standard deviation of the array is 
2 = vr^^. 
* Cf. Yule, loc. cit. 
