CORN AND HOG CORRELATIONS 53 
The total annual western pack is the sum of the summer and fol- 
lowing winter packs. In round numbers the path coefficients have 
the values +0.60 and +0.55, respectively, giving about 100 per cent 
determination. 
TOTAL EASTERN PACK 
The eastern pack occupies a rather isolated position among the 
variables discussed in this bulletin. In a general way its fluctuations 
are parallel to those of western pack, and the common influence of the 
factors determining the latter can be represented by a path coefficient 
leading from it. As pointed out, eastern pack is even more closely 
correlated with western hog price than is western pack. This was 
interpreted as due to an influence of western price on eastern ship- 
ments rather than of eastern supply on price. There is, in fact, a 
high correlation with the price of the preceding winter as well as with 
the prices of the summer and winter of the year in question. The 
following path coefficients were found by trial to give the best ap- 
proximations to the correlations involving eastern pack. 
Eastern pack 
Western pack +0.25 Winter price' —0.25 
Summer price —0. 25 
Winter price — 0. 20 
These four factors account for 56 per cent determination. The 
large residual variation is doubtless dependent on special eastern 
conditions not dealt with here. 
FARM PRICE OF HOGS, JANUARY 1 
The lag of farm price of hogs on the packer's price has been dis- 
cussed. TPath coefficients of + 0.30 and + 0.70 leading from the pack- 
ing prices of the preceding summer and the current winter give a 
fairty satisfactory fit to its correlations and account for 86 per cent 
determination. 
THE CORRELATIONS 
The correlations which result from the foregoing system of path 
coefficients are easily calculated. Those within the central system 
are given in Table 9. The next step is to find the correlation between 
summer and winter slaughter and weight on the one hand and the 
variables in the central system, including crop, on the other. The 
correlation between winter weight and the crop of the preceding 
fall is, for example, +0.35 r B c + 0. 65. The remaining correlations 
can now be calculated directly. As an example, that between 
winter pack (G) and another variable (X) is obtained from the 
formula, 
r XG = +0. 85 rxB' + 0. 35 r XB " + 0. 15 r XB -~0. 20 r xc 
The correlations which result from the system of path coefficients 
are given in italic in Tables 3 to 6, inclusive, each following the 
corresponding observed correlation. The average difference between 
the observed and expected correlations (neglecting sign) is 0.09, 
which is about as good agreement as can reasonably be expected. 
The most serious discrepancies come in certain correlations involving 
corn acreage and yield, which were intentionally neglected for the 
sake of avoiding complexity in the relations among the more im- 
portant variables. The degree of correspondence between observa- 
