54 BULLETIN 1300, U. S. DEPARTMENT OF AGRICULTURE 
tion and expectation for the more important variables is shown in 
Figures 16 to 25, inclusive. The observed correlations are shown as 
solid lines and the expected as dotted lines. 
The assumed system of causal relations gives a fairly satisfactory 
explanation of the 510 observed correlations. Is it the only hypo- 
thetical system which could do this? A great many other central 
systems were tried. The writer started, for example, with the 
belief that there should be an important direct influence of western 
summer and winter wholesale packs on the prices paid by the packers 
for these same hogs. No scheme which embodied this conception 
was even approximately as successful as that here presented. 7 The 
same is true of all other systems tested. The successful system is 
based on the analysis of the factors which give the maximum per- 
centage determination of each variable, according to Pearson's 
method of multiple correlation, rather than on preconceived ideas 
of what the relations ought to be. From this analysis and the 
numerous tests of other systems, the writer feels confident that no 
equally simple system can be found which differs substantially from 
the present and gives even approximately so good a fit to the observed 
correlations. Doubtless slight improvement can be effected by 
small modification in the value of the path coefficients or in the 
addition of minor paths. A slightly different interpretation could 
doubtless be given to some of the paths here adopted. The actions 
and reactions among the variables are necessarily too complex to 
be represented more than roughly by any simple diagram. 
PREDICTION FORMULAS 
The coefficient of correlation between two variables expresses the 
average amount which either one deviates from its trend on the 
occurrence of a given deviation of the other, provided that the devia- 
tion of each is measured in terms of its own standard deviation, or, 
theoretically, any other sort of average deviation. Thus, if the corn 
crop is an average amount above the trend, we find in Table 3 or 
Figure 16 that corn price is in general below its trend by 80 per cent 
of the average amount of its fluctuation. Similarly, after an average 
deviation of the corn crop, the hog pack of the next summer will be 
about 61 per cent of the average fluctuation above its trend. Thus 
everyone of the correlations in Tables 3 to 6, inclusive, can be used as a 
prediction formula. In order to convert such a prediction formula, 
expressed in terms of average fluctuation, into actual units, it is of 
course merely necessary to multiply by the ratio of the standard 
deviations. The latter are given in Table 2 for the period from 1889 
to 1913 and for the whole period 1871 to 1913 when the data were 
available. 
For the probable deviation of X in terms of Y (regression of X on 
Y) we have 
a 
7 It is, however, probable that a direct (negative) influence of pack on price could be represented with 
some improvement to the system, if a reaction (positive) of price on the same season's pack was also repre- 
sented. With such a system of relations it can be shown that price may be more closely correlated with 
the factors back of pack than with pack itself. The treatment of such reciprocal relations between vari- 
ables requires an extension of the theory of path coefficients. It will suffice here to point out that the 
relations between pack and price could probably be more accurately shown, but at the expense of con- 
siderable additional complexity in the system. 
