INPUT AS RELATED TO OUTPUT 
43 
CURVILINEAR CORRELATION 
The fact that output does not increase in constant proportion to 
increases in input, the economic law of diminishing returns, is 
especially true of agricultural production. Obviously, then, if all but 
one input factor were held constant, and regularly increasing quan- 
tities of that one factor were applied, the increases in yield would not 
be exactly proportional to the increases in that input but would be 
progressively smaller and smaller. The relation between the input 
and the output is hence not linear; each unit increase in input does 
not produce the same increase in output. Instead the relation is 
curvilinear; the increase in output is different for each specific in- 
crease in input. 
How can this relation be measured statistically ? Simple or multi- 
ple linear correlation will reveal the average effect of variations in 
each input factor. Figures 14, 15, and 16 illustrate the limitations 
Com Fed and Pork Produced; Combined Group 
<250 
200 
150 
100 
50 
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1 
5 10 15 20 
BUSHELS OF CORN FED PER PIG AFTER WEANING 
©=GROUP AVERAGES 
(Z'/2 BUSHEL CROUPS) 
25 
Fig. 16. — The gain per bushel of corn is cot constant. Combining the two groups shows 
that, as the hog becomes heavier, the increase in weight for each bushel of corn con- 
sumed becomes less 
in using linear correlation for this purpose. Both Figures 14 and 
15 show the relation between corn fed to pigs and the resulting gains 
in weight; but Figure 14 has relatively more records below 12 
bushels of corn than has Figure 15. It will be seen that the slope of 
the regression line indicating the average gain from a bushel of 
corn is steeper in Figure 14 than in Figure 15, each additional 
bushel of corn being accompanied by an average gain of 9.4 pounds 
in the former group, but only 7.2 pounds in "the latter group. 
Figure 16 shows the groups combined. 21 The farms were sorted 
according to the quantity of corn fed, and the average corn and pork 
for each of these groups indicated on the chart. A curve has been 
drawn, free-hand, approximately through these averages to indicate 
31 In order to insure comparability, the farms shown in Fisrures 14 and 15 were both 
selected from those shown in Figure 16, the lower group by discarding half of the farms 
with corn inputs above the average and the higher group by discarding half of the farms 
with inputs below the average. Hence, although there are 31 farms shown on each of 
the separate groups, there are only 43 shown in Figure 16. 
