1086 
Journal of Agricultural Research 
Vol. XXX, No. 11 
tion. Prom these curves the depend¬ 
ents are again estimated by readiilg 
from the curve the yield value associ¬ 
ated with each given weather value. 
New residuals are obtained and plotted 
as deviations from the regression 
curves, and the process is continued 
until the residuals can not be reduced 
further. It is seen that this method is 
one of approximation and as such is 
not susceptible to the mathematical 
demonstration of validity and proba¬ 
bility as are many other statistical 
methods. On the other hand, as meas¬ 
ured by the closeness with which the 
actual yield may be estimated from the 
independent factors and by empirical 
tests, the method is considerably supe¬ 
rior. Linear correlation is not a satis¬ 
factory method of analysis when the 
theory predicates nonlinear relation¬ 
ships, that is, optimum conditions. 
For the purpose of obtaining the best 
trend line, time was treated as an inde¬ 
pendent variable in this analysis. 
When the curvilinear analysis just 
described is completed, the net func¬ 
tional relationship between the weather 
factors and yield is described by the 
resulting curves. These curves are 
charted in Figure 1. By reading from 
them the yield deviations from trend 
(ordinates) associated with the given 
weather factors measured in any given 
season (abscissae), and by summing 
these readings and subtracting the con¬ 
stant, 2.0, an estimate of the yield may 
be obtained, expressed as deviation 
from normal or trend value. This can 
be done early in September, thus giving 
an unusually close estimate of the final 
ield at a comparatively early date, 
uch estimates were worked out for the 
period studied, and the curve so ob¬ 
tained is shown on the chart. With the 
omission of two years, 1911 and 1912,' 
where there is a most pronounced re¬ 
covery in the yield figure, the correla¬ 
tion index 6 between the actual and the 
estimated is unusual (0.97), the stand¬ 
ard error of estimate being but a fourth 
of the standard deviation of yield from 
trend. 
Two considerations tend to diminish 
the reliability of forecasts made from 
these curves. In the first place there 
are very few observations upon which 
to base the curves. There are about 
20 years which have been used to es¬ 
tablish five separate functional rela¬ 
tionships. The correlation is probably 
in some degree due to the mere numeri¬ 
cal probabilities of adjusting these 
functions to observations. This influ¬ 
ence, however, is probably slight, since 
the correlation is so unusually high and 
since the curves represent relationships 
which are in accordance with the con¬ 
ception of what the effect of weather 
factors should be. For example, the 
curves indicate that there is generally 
too much rain during the June-to- 
August growing period, since an in¬ 
crease in rainfall is accompanied by a 
decrease in yield. This furnishes sup¬ 
port for the proposition that an in¬ 
crease in rainfall increases the activity 
of the weevil and hence increases crop 
damage. 
In the second place, during the first 
few years of the period covered there 
was but slight boll-weevil infestation. 
In 1909, however, practically all of 
Louisiana was infested. The weather 
is considered an important factor in 
the life of the weevil. Thus what 
would normally be good weather for 
cotton growing might be the reverse 
under infestation, because such weather 
might favor weevil propagation; that is, 
the influence of weather factors when 
operating on the cotton plant through 
the weevil would be different from the 
influence when these factors were 
operating directly upon the plant. 
The curves, then, contain the results 
of two mixed influences, one of which 
is now predominant. To avoid this 
mixture through shortening the period 
by limiting the analysis to those years 
subsequent to 1908 is to so greatly 
increase the first possibility of error 
mentioned as to render any curves 
practically invalid. But as an experi¬ 
ment, a linear multiple correlation 
coefficient was obtained for the years 
1908 to 1922, inclusive, using June and 
August rainfall and August tempera¬ 
ture as the independent variables. 
This coefficient was 0.755. It could 
undoubtedly have been higher if 
curves had been used, but it was felt 
that the data were insufficient to 
justify the use of curves. The regres¬ 
sion equation arrived at is given below, 
A referring to June rainfall, E to 
August rainfall, and F to 1 August 
temperature. 
Yield=919.38 — 11.43A-0.74S—8.69F 
Of the three factors involved, A is 
the most important and E the least. 
The regressions are all negative, as 
the curves were, when derived from 
the longer series. This serves as a 
partial indication of the predominance 
of the weevil influence in determining 
the curves, and therefore encourages 
the placing of confidence in the curves. 
« Ezekiel, M. 1 . B. a method of handling curvilineak correlation for any number of varia¬ 
bles. Jour. Amer. Statis. Assoc. 19: 431-453, illus., 1924. 
