46 BULLETIN 1300, U. S. DEPARTMENT OE AGEICULTUEE 
It can be shown that the squares of the path coefficients measure 
the degree of determination by each cause. If the causes are inde- 
pendent of each other and all are accounted for, the sum of the 
squared path coefficients is unity. If the causes are correlated, terms 
representing joint determination must be recognized. The complete 
determination of X in Figure 1 by factors A. B, and C can be expressed 
by the equation 
(1) a--\-l 2 -rC 2 -2lc r BC = l 
where a. b, and c are the coefficients for the paths indicated in the 
diagram. 
The squared path coefficients and the expressions for joint deter- 
mination measure the portion of the squared standard deviation due 
to the causes singly and jointly, respectively. 
The correlations between two variables can be shown to equal the 
sum of the products of the path coefficients along all the paths by 
which the variables are connected. In Figure 1. X and Y are con- 
nected by 4 paths X-B-Y, X-C-Y, X-B-C-Y, and X-C-B-Y. 
Taking the products of the path coefficients and the correlations (which 
represent the resultant of path coefficients) along each of these paths 
and adding, we have 
(2) rxY=#&' + cc ; -fft/'Bcc'-f- cr B cb' 
Equations 1 and 2 can be expressed more compactly in the following 
forms obtained by application of equation 2 itself. 
(la) ar KX -r-br B x J rcr C x = l 
(2a) / 'xt = h by + ctcy 
The method of analysis to be used here consists in equating each 
observed correlation to the system of path coefficients responsible 
for it. as in Equation 2. or in expressing complete determination of 
one variable by others, as in Equation 1. 
CENTRAL SYSTEM OF RELATIONS 
It would be hopeless to attempt to deal with all the variables at 
once at the outset. Those which are most fundamental should be 
dealt with first in a central system; those with least causal influence 
on the others being ultimately related to this system peripherally. 
Among the corn variables, the price has in general the closest 
correlations with the hog variables and is thus the best one to take 
as representative of the influence of corn on hogs, although the most 
dependent variable within the corn system itself. 
The most fundamental factor in the hog situation is the amount of 
breeding. There are no calculated correlations between breeding 
and the other quantities, but evidence has been found that summer 
weight is a close indicator of the amount of breeding in the same year, 
although also influenced by the breeding in the preceding fall and 
perhaps to some extent by the amount of corn m relation to the 
number of hogs. Of course the winter slaughter a year and a half 
later is also, to a considerable extent, an indicator of the amount of 
breeding. 
