34 BULLETIN 1440, IT. S. DEPARTMENT OF AGRICULTURE 
X 9 Time (numbering months from 1 up). This allows for changes in con- 
sumption habits and other changes in demand with the passage of time. 
Xio The Bureau of Labor index of wholesale prices for all commodities (here- 
after referred to as the "Bureau of Labor Index"). (17). 
Xn The price of hogs, not adjusted in any way. 
The data were taken monthly, giving 90 observations. 
Factors Xi, X 2 , and X 3 were included as different measures of the 
influence of supply; factors X 4 , X 5 , X 6 , X 7 and X 8 as forces influencing 
demand; X 9 to allow for any trend in price apart from that accounted 
for by the factors stated; and Xi to adjust for the effect of changes 
in the value of money upon hog prices. 
Since practically all of the factors were thought to have a relative 
rather than an additive relation to price, all of the factors except 
X 9 , time, were stated as logarithms (6). 
Correlating the factors thus stated, a multiple correlation of 
hog prices with the 10 other factors of R = 0. 936 was obtained. 
Correcting this to take account of the fact that 10 constants were 
determined with only 90 observations, 15 the true multiple correlation 
is reduced to 0.928. 
The regression equation is as follows: 
(1) log Xn= -0.09443 log Xj + 0.15888 log X 2 -0.21986 log X 3 -0.23675 
log X4-0.07250 log X 5 + 2.23777 log X 6 +0.04759 log X/ +0.22659 log X 8 - 
0.03036 X 8 + 1.63099 log X 10 -K. 
The value of the constant (K) in this equation varies according 
to the units in which the different variables are expressed. 
The variable Xi represents the price index, so moving the regres- 
sion value for that variable to the left of the equality sign gives the 
regression equation for the prices deflated according to the observed 
relation. 
The fact that the best fit is obtained by dividing the actual prices 
by the price index raised to the 1.63 power may mean that hog prices 
are more sensitive to variations in the price level than are most com- 
modities. For example, on this basis a change from 100 to 125 in 
the wholesale prices of all commodities would mean a change from 
100 to 144 in hog prices, and a change from 100 to 75 in wholesale 
prices would mean a change from 100 to 63 in hog prices. However, 
it is possible that part of the effect of changes in business activity 
upon hog prices is reflected in this relation, the index of wholesale 
prices being itself one measure of business activity. For this reason 
this particular solution, though giving a very good correlation with 
actual hog prices over the period, does not give a satisfactory basis 
for getting a demand curve. 
It should be noted that the net regressions shown in equation 1 
show a larger effect for changes in storage, variable X 4 , than they do 
for changes in X x , X 2 , or X 3 , the three variables representing supply. 
As the stocks in storage vary rather closely with the supply, much of 
the real effect of the quantity supplied upon prices is shown as a 
response to variations in this storage factor. That is, the fact that 
the use of storage irons out the differences in supply from period to 
period obscures to some extent the basic relation between supply 
and price. 
where m= number of constants, and n= number of observations. {21, p 41 .) 
1— m/n 
