42 BULLETIN 1440^ U. S. DEPARTMENT OE AGRICULTURE 
Adding X 20 to the independent variables, a very high correlation 
with the price was obtained, B.17. 15,16,20 = 0.993. This would neces- 
sarily be so, since the index of demand was simply the residual from 
the correlation of X 15 and Xi fl with X 17 , expressed as a percentage. 
This very high correlation therefore has no real significance of itself. 
As will be shown directly, however, the index of total demand has 
a multiple correlation of 0.81 with factors which logically should 
affect demand. This means that 66 per cent of the variation in 
the index of demand can be accounted for on the basis of other 
factors. Since the net correlation of X 20 with X 17 is necessarily 
very high — ri 7 , 20 . 15,16 = +0.994 — substituting an index of demand 
estimated on the basis of the relatonship of the computed index to 
independent factors would give a correlation with price much above 
that obtained when no measure of demand was included. If the 
66 per cent of the index that could be estimated was as closely re- 
lated to the price as was all of the original index, a multiple coefficient 
of about 0.94 would be obtained by correlating receipts, time, and 
the new index with prices. 
RELATIVE IMPORTANCE OF THE VARIOUS FACTORS AFFECTING THE PRICE 
Having computed this index to measure the combined effect upon 
price of all the demand factors, at least in a rough way, the next 
step was to measure the portion of the variation in hog prices which 
could be ascribed to the effect of each factor. 
The factors considered were : 
Xi 5 Receipts of hogs at 11 markets, 12 months moving average. 
X 16 Time. 
X 2 o The index of total demand. 
X 2 i Difference between actual hog prices and hog prices divided by Bureau 
of Labor Index. 
X22 Seasonal variation in hog prices times trend in prices minus the trend of 
prices. 
X23 The price of heavy hogs, not adjusted in any way. 
The figures were taken monthly for the period 1904 to 1915, 
inclusive. 
Variable X 22 represented that part of the hog prices, in dollars and 
cents, which could be explained on the basis of the regular seasonal 
variation in price. Similarly variable X 2i represented that part of 
the actual prices which could be explained on the basis of changes 
in the value of money. And as has been shown, variable X 2 o was a 
rough measure of the variation in demand factors. 
The five independent factors had a multiple correlation with the 
actual prices of R = 0.985. As stated before, this high correlation is 
not of itself significant, since the. index of demand used in this correla- 
tion was itself computed from the price. Had the variation in 
demand been expressed as the absolute difference between the actual 
price and the computed price, perfect correlation (11 = 1.00) would 
necessarily have been obtained, since that would be adding the 
residual as an independent factor. The failure to obtain this perfect 
correlation resulted from expressing the difference on a percentage 
basis. Even leaving out this factor, however, the correlation was 
R =0.904. The net correlation of the index of demand with the price 
was 0.918 ; that is, the index accounted for 84.3 per cent of the variation 
in price left after eliminating the effect of the other factors. 
