WHAT MAKES THE PRICE OF OATS 
19 
be more accurate as a basis for estimating the seasonal trend of prices 
than is the average annual price heretofore used. That the Sep- 
tember price can be predicted with greater accuracy than the annual 
price is shown by the fact that a correlation coefficient of —0.85 is 
obtained when the year-to-year changes in the September cash price 
are correlated with the changes in the final estimate of oat production 
of the Department of Agriculture as compared with a coefficient of 
— 0.82 when the annual price is used. If to the production figure is 
added the carry over from the previous year, and changes in this new 
figure representing supply are correlated with changes in the Sep- 
tember price, a coefficient of —0.91 is obtained. 19 Figure 8 repre- 
sents graphically the close relationship between production and the 
September price. 
DISCUSSION OF METHOD 
As indication of the relative effectiveness of using percentage 
changes as compared with absolute changes in correlating the Sep- 
tember price with production plus carry over, four correlations were 
carried out, using different combinations of the two methods. The 
resulting coefficients are given in Table 10. 
Table 10. — Correlation of changes in September price and production plus carry 
over of oats, 1896 to 1913 
Variables 
(o) Price: Percentage change over that of the preceding year 
(6) Production plus carry over: Percentage change over that of the preceding year . . 
(a) Price : Change in cents per bushel over that of the preceding year 
(5) Production and carry over: Percentage change over that of the preceding year... 
(a) Price: Change in cents per bushel over that of the preceding year 
(b) Production plus carry over: Percentage change over the average figure of the 
preceding and current years 
(a) Price: Change in cents per bushel 
(6) Production plus carry over: Change in tens of millions of bushels 
1 Approximate standard error 18.6+per cent of average price, 33 cents. 
Coeffi- 
cient 
-0.74 
-.90 
-.90 
Standard 
error 
Cents 
6.1 
3.8 
3.8 
3.5 
A correlation using absolute changes (first differences) does not 
require the elimination of a straight-line trend which may be present, 
for this method of correlation is itself a method of eliminating such 
trends, owing to the fact that the trend affects the change from year 
to year by a constant amount. Adding a constant to a series does 
not affect the deviations from the average of the series, since each 
item is increased as much as any other and the relationship between 
them remains the same. 20 It is necessary, however, in first difference 
correlations, to make corrections for nonlinear trends which may 
disturb the price series, either by dividing each price item by its 
16 A correlation for the period 1895 to 1915 gives a coefficient of 0.94 when the September cash price, the 
Bureau of Labor Statistics all-commodities index number for September, and the final estimates of pro- 
duction plus carry over were correlated as changes over the values for the preceding years. Expressing 
changes in the average September price in cents per bushel as xi; changes in the index number as xi ; and 
changes in the estimated production, plus old stocks on farms August 1, plus visible supply July 1, in 
10,000,000 of bushels, as xz, the estimating equation is zi=0.388 xi — 0.446 x%. Applying this equation to 
the 20 years covered by the correlations, an average error of 3 cents per bushel in predicting the September 
price is found. This may be compared with the average error of 3.6 cents in predicting the annual price. 
(See p. 12.) The error is less than 3 cents for 13 of the 20 years. 
20 B. B. Smith. The use of punched card tabulating equipment in multiple correlation problems; 
collected and prepared for the use of statisticians of the Bureau of Agricultural Economics, U. S. Depart- 
ment of Agriculture. 1923. Mimeographed. 
