INPUT AS RELATED TO OUTPUT 41 
MULTIPLE CORRELATION 
The correlation of two variables (gross or simple correlation) 
determines what value of one variable may be expected to accom- 
pany a given value of the other, and further gives a measure of 
how close the relation is. 
The case of feeding pigs will be used for an illustration. Figure 
14 is a dot chart showing the average quantity of corn fed per pig 
on each of 31 farms, 18 and the gain in weight made on the average 
for each farm. It is at once evident that the more corn the hogs 
received, the more gain they made. Determining the regression of 
weight on corn fed, we find the straight line indicated, which shows 
that on the average each additional bushel of corn fed the hogs 
was accompanied by a gain of 9.4 pounds in weight. 19 However, 
the pigs received other feed in addition to the corn — oats, mill feed, 
and tankage being most common. The gains made were due, there- 
fore, only in part to the corn, the remainder being due to the other 
feed. Further, the average gain which accompanied the consump- 
tion of a certain amount of corn was not the net gain due to corn ; 
it was the gain due to the corn plus the accompanying feeds. 
The problem is to find, not how much gain accompanied the con- 
sumption of a given amount of corn, but how much of that gain 
was clue solely to the corn fed, eliminating gains due to the other 
feeds. Multiple correlation is the only method which can give us 
this result. Considering the corn, oats, tankage, and mill feed 
used, an analysis by multiple correlation gives the following infor- 
mation : 
(1) The average gain in pork per additional bushel of corn fed, 
eliminating the gain due to the oats, tankage, and mill feed which 
was fed along with the corn — (net regression of pork on corn). 
(2) The average gain in pork per additional bushel of oats fed, 
eliminating the gain due to corn, tankage, and mill feed — (net re- 
gression of pork on oats). 
(3) The average gain in pork per additional hundredweight of 
tankage fed, eliminating the gain due to corn, oats, and mill feed — 
(net regression of pork on tankage). 
(4) The average gain in pork per additional hundredweight of 
mill feed fed, eliminating the gain due to corn, oats, and tankage — 
(net regression of pork on mill feed). 
(5) A formula for estimating the pork production to be expected 
from feeding any given combination of corn, oats, tankage, and 
mill feeds (the net regression equation), and a measure of the 
probable accuracy of such estimates (the multiple correlation of 
pork with all four feeds). 
The use of this method secures results from the farm data compar- 
able with those obtained under experimental conditions. In an ex- 
periment all factors are held constant except the one Avhose eifect it 
is desired to measure. This can not be done under farm conditions. 
18 From records secured in Illinois and Iowa by the Division of Cost of Production, Bu- 
reau of Agricultural Economics, U. S. Department of Agriculture. 
18 References on simple linear correlation: 
Tolley, H. R., and S. W. Mendum. Method of Testing Farm Management and Cost of 
Production Data for Validity of Conclusions, U. S. Department of Agriculture Circular 
307. 1924. 
King. Willford I. The Elements of Statistical Method, pp. 197-202- 13-215. 1919. 
Kelley, Truman L. Statistical Method, pp. 179-185. 1923. 
Yule, G. Udny. An Introduction to the Theory of Statistics, pp. 157-209, 352 ; 1922. 
(Sixth edition.) 
