60 BULLETIN 1400, U. S. DEPARTMENT OF AGRICULTURE 
(3) Making the same computation with other possible price 
conditions to determine the most profitable combination under 
other conditions {20). 
The following factors were used in the analysis : 
A. Therms of net energy consumed per cow per year (exclu- 
sive of pasture). 
B. Ratio of digestible protein (in pounds) to net energy (in 
therms) . 
C. Butterfat test of milk. 
D. Proportion of the herd freshening in the fall. 
E. Average value per cow (to measure quality). 
Each factor was expressed in logarithms, to obtain "multiplying" 
relationships (6). 
Using solid multiple curvilinear correlation, an index of multiple 
correlation of P=0.615 was obtained with milk production for the 
year. 
One important reason why the correlation was not higher was that 
it was not possible to obtain any satisfactory measure of the contri- 
bution of pasturage to milk production. Estimates of pasturage 
based on length of time the cows were on pasture and the acres of 
pasture per cow gave results of no significance on correlation, but 
correlation with winter milk production indicated that the other 
factors included were responsible for at least half the variation in 
milk production while the cows were not on pasture. 23 
With the low correlation obtained, neither the regressions nor the 
relative determination by the different variables constituted a very 
exact measurement, and they are therefore not presented separately 
at this point. The regression curves, however, did furnish a means 
for at least approximately eliminating the effect of other variables 
from the tables showing the relation of various factors to the feed 
cost of milk production, and they were therefore used for this purpose 
in preparing Tables 27 to 31, and in estimating the most probable 
milk production for the rations given in Table 27. 
The results secured in this study of the dairy enterprise fell far 
short of perfect correlation, but they did serve to eliminate from these 
tables the effects of such other variables as could be measured. In- 
stead of assuming that "all other factors" would average out, so 
that the tables would be significant, this merely assumes that varia- 
tions due to unmeasured factors will tend to average out. To that 
extent the tables are both more significant and more reliable than 
similar results obtained by merely sorting and averaging. 
The tables following, 50 to 54, show averages of the labor index, 
crop index, crop acreages, pasture acreages, and crop acres per cow, 
for farms sorted by number of cows and dairy index. Comparing these 
tables, with Table 22, page 24, gives a direct comparison of the 
influence of these different factors upon the operator's earnings shown 
for these groups of farms. 
2 The four factors A, B, C, and D, gave a coefficient of multiple correlation of #=0.646 with the produc- 
tion for the winter alone. Since these four variables had only given #=0.553 on linear correlation with 
production for the year, it is likely that application of the curvilinear method to the winter production 
alone would have raised the correlation to about 0.72, since (0.553) 2 : (0.615) 2 = (0.646) 2 : (0.719) 2 
