8 
BULLETIN 1351, U. S. DEPARTMENT OF AGRICULTURE 
deviation squared. Ratios to trends are used here as a method of 
eliminating the influence of the upward tendency of production and 
the downward and upward trends of price which would partially 
obscure the relationship between the two factors and result in a, 
lower coefficient of correlation. 
To predict the average annual price of oats when the production 
is known, an ''estimating equation" must be worked out from the 
results obtained in the correlation. This equation has the form 
y = a + hx, in which y is the price to be estimated, x is the production 
during the given year, and a and b are constant terms that must be 
PRICE 
RATIOY 
1.5 
1.4 
1.2 
3 
y 
Y 
= **«« £ Z29 (*- 

-19 +1.19* 
X- .7 Lj=I.SS 
x= .a H = ,. 3 , 
*= ■» V = U3 
x= i.o y = i.oo 
X= I.I y - A3 
*='•* 7 J =- ao 
i 
\ 
• 
, 
/ 
; 
r~ 
• \ 
s. 
i 
\ 
* 
• 
•\ 
' 
• 
' VVc 
• 
• 
V. 
1 1 
5 .6 .7 .8 .9 1.0 I.I 1.2 1.3 \A 
PRODUCTION RATIO =X 
Relation between price and production ratios shown as a curved line 
15 
I 6 
Fig. 3.— A curved line describes the relation between price and production better than does a straight 
line. If the relation were perfect, all of the dots in the scatter diagram would fall exactly on the line. 
The curve in this figure is described by two formulae, a reciprocal formula used by Working coinciding 
with an exponential formula used by Moore 
calculated from the data. A coefficient of 0.82, however, is not 
large enough to give sufficiently accurate results in forecasting prices. 
Other factors must be considered in addition to production, so that 
more of the variation in price will be accounted for than that due 
to production alone. 
The equation just given assumes that the relation between the 
two factors is expressed graphically by a straight line; that is, that 
regardless of the size of the factors, a given change in one is always 
associated with the same estimated change in the other. Consider- 
ation of the theory of elasticity of demand and the concept of di- 
minishing utility suggests that a straight line may not represent most 
