12 
BULLETIN 1351, U. S. DEPARTMENT OF AGRICULTURE 
An estimating equation may now be calculated from the data 
which gives the highest correlation with price. The equation is 
Zi = 4. 20 + 2. 03 x 2 — 1.16 x 3 . Here x ± is the percentage change in 
price per bushel over that of the previous year; x 2 is the percentage 
change in the index number; and x 3 is the percentage change in the 
production of the United States plus carry over. 14 
Figure 4 is a comparison of the annual prices as estimated from 
the equation just given and the actual prices during that period. The 
average error for the 22 years is 3.6 cents, or 9.8 per cent of the aver- 
age price. 
In the correlation just described changes in the price level were 
taken account of by using the index number of prices of farm products 
as a separate variable. Approximately the same results would be 
PRICE 
CENTS 
PER BU. 
90 
80 
70 
60 
50 
40 
30 
20 
1 

/<< £ 
%ti mated price 
V 
* Actual price 
/ \> 
/ V 
'-^ 
V 
V 
*^z^Z- 
V 
i i i 
I 1 1 1 
1 1 1 1 
189 
6-'97 
190 
0-01 190 
5-06 
I9IC 
-II 
I9IE 
-16 
1920-21 
A comparison of the actual price of oats at Chicago with the price estimated by the use of the estimating 
formula 
Fig. 4.— The accuracy with which oat prices may be estimated by use of the formula developed in this 
bulletin is indicated. The inaccuracy during certain years may have been due to unusual changes in 
demand, to inaccuracy in the estimate of production, or to other factors not accounted for in the esti- 
mating equation 
secured by dividing the price of oats by the corresponding index 
number. 
The variables were expressed as percentage changes over the pre- 
ceding year because it was impossible to extend satisfactory trends 
through the war years. The difficulty will be recognized by an inspec- 
tion of the price and production graphs in Figure 1. A first difference 
or percentage change over the previous year is more or less free from 
cumulative error, and may be used satisfactorily in such a situation. 
Percentage changes, however, are subject to a type of error similar 
to that described by Fisher in "The making of index numbers " 15 
that is, rising prices tend to augment the percentage changes, whereas 
falling prices have an opposite effect. It may be possible to correct 
this error by the use of percentage changes over the average of the 
figures for the current and the preceding years. 
" See Table V, Appendix A, p. 33, for the method of estimating prices by the use*of an estimating 
I' Irving Fisher. The making of index numbers. 1922. 
