50 BULLETIN" 1300, U. S. DEPARTMENT OF AGRICULTURE 
The correlations which result from these path coefficients are 
given in the last column in Table 9. In the diagram (fig. 27) the 
positive paths are marked with crosses. The three highest coefficients 
(c, d, m) are shown in heavy lines and the three lowest (e, f, g) are 
shown in dotted lines. With these considerations in mind, the 
influence of corn on the hog situation and the tendency toward 
reversal in the amount of breeding every two years are clearly brought 
out. 
Calculating the coefficients of determination, it is found that breed- 
ing is determined 73 per cent by the factors represented, leaving 27 
per cent residual; summer price is determined 77 per cent, leaving 
23 per cent residual; and winter price 82 per cent, leaving 18 per cent 
residual. It will be recalled that in the four cases in which there 
was known to be complete determination — crop by acreage and 
yield, total western slaughter by western summer and western winter 
slaughter, summer pork production by summer slaughter and summer 
weight, winter pork production by winter slaughter and "winter 
weight — the sums of the coefficients of determination amounted to 
86, 96, 95, and 90 per cent, respectively. Thus about 9 per cent 
spurious determination is to be expected as the result of such condi- 
tions as inconsistencies in fitting the 
-^**i^k>c graphs, nonlinearity and nonadditive 
^ lSs ^^l combination of effects. It follows 
ti^O ~~ <3€> i r r that our fundamental hog variables, 
JjJ!##'** r breeding and summer and winter 
^j^^^sbn prices, are probably really determined 
^gp about 86 per cent on the average by 
ttt„ oa n l . Bimi j tt a i.« M ..w-»» 1 » n the factors in the diagram instead of 
Fig. 28.— Diagram of the relations between corn 1 & 
acreage (A), yield (Y), crop (C), and price about 77 per Cent as actually IOUnd 
SmcSnt e s SSStaSS valUeS ° f the Path by the foregoing analysis. It follows 
also that, all other factors combined, 
including such factors as the effects of epidemics of disease, can only 
determine from 14 to 23 per cent of the variation of these hog vari- 
ables about their trends. 
The relations between the corn variables are represented approxi- 
mately in Figure 28. 
In analysis of the corn situation for its own sake, it would be well 
to take account of the correlation between the acreage of successive 
years ( + 0.36) and possibly the indications of negative correlations 
between successive yields ( — 0.15), and crops ( — 0.20), as well as 
certain other obscure indications. There is probablv also a slight 
degree of determination by the preceding hog situation. None of 
these relations have an important bearing on the hog situation, 
however, so that for the present purpose this simple scheme of rela- 
tions is adequate. The crop is represented as completely determined 
by acreage and yield (12 per cent by acreage, 81 per cent by yield). 
Price is determined 64 per cent by crop, leaving 36 per cent residual. 
The theoretical correlations between crop and various hog variables in 
Figure 27 can be obtained by multiplying the corresponding price 
correlation by —0.80. Similarly, the theoretical correlations in- 
volving acreage and yield can be obtained by multiplying the crop 
correlation by +0.45 and +0.90, respectively. 
