Raymond Pearl 
53 
It is seen at once that r/ differs from r and S^j from zero in all cases. 
This, of course, implies departure of the system from linearity. But evidently 
deviations of a system from linearity may be due to either one or both of two 
causes. Either, on the one hand, the system may be truly non-linear, in which 
event the means of the ariays will be fitted better by some curve than by a straight 
line, or, on the other hand, the points fixed by the means of the arrays may not 
lie exactly on a straight line and still no curve will represent the relationship 
between the two variables concerned better than a straight line so drawn that the 
mean square of the deviations of the points from the line is a minimum. In the 
first case we have true non-linearity of the regression, while in the second the 
deviation from linearity is due to the errors of random sampling, and it might 
reasonably be expected that if the whole population could be studied the regression 
would become strictly linear. Now evidently in both these cases rj will differ 
from r and from zero, so that recourse must be had to some further method 
in order to determine into which class a given case falls. Two such methods 
immediately suggest themselves: one, to examine the probable errors involved, 
the other, to inspect the fitted regression line. 
An examination of Table XIV makes it immediately evident that the differ- 
ences between rj and r (without regard to sign) give values of the same order of 
magnitude as the probable errors of r. In only one case is this difference as 
great as three times the probable error of r, and in the great majority of cases it 
does not approach such a value*. So then it seems probable that in our series the 
regression of brain-weight on age is linear within the errors arising from random 
sampling. The approach to linearity is sensibly the same both for the whole 
period of adult life and for the younger half of this period. 
In order to bring out the facts graphically I have had prepared a series of 
diagrams showing the regression lines for brain- weight on age. For the sake of 
economizing space, and since there is essential agreement between the different 
series with respect to 77, it was decided not to publish all the regression diagrams. 
I have chosen for representation here the regression lines for the Swedish and the 
Hessian data. These are shown in Diagrams II to IX. 
D1.A.GRAM II. Probable Brain-weight for given Age. 
Swedish s Total. 
g 
s 
< 
) . 
( 
— ___J 
) 
< 
^ ( 
) 
' ( 
r~ — 
( 
) 
22 5 27-5 32 5 37 5 42 5 47 5 52 5 57 5 62 5 67 5 72 5 77 5 
Age ( = A) in years. 
[* The proper test is the probable error of ~ r, which we hope will shortly be published. Ed.] 
