INPUT AS RELATED TO OUTPUT 11 
Table 9. — Net effect of various conditions on grain fed per day 
On the average, for each additional- 
Grain fed 
per day 
was in- 
creased— 
Closeness of the 
relation 
30 days on feed 
100 pounds initial weight... 
Pound of roughage per day. 
Pounds i 
— 1. 55 
1.51 
.005 
r=-0.259± 0.077 
r=+0. 321 ±0.074 
r=+0.005±0.0S2 
1 Decrease is indicated by a minus sign (— ). 
Table 10, calculated from the values in Table 9, shows what 
would be the average input of grain per day under 20 different 
conditions. It should be remembered that these 20 inputs are based 
upon records from only 67 cases; but because of the method of 
computation, each of these 20 inputs is based upon all 67 cases, 
instead of upon only the very few droves which happen to fall 
within any one of the 20 classes. 
Table 10. — Computed average input of (train per head per day, oy initial 
iceight of animal and length of feeding period 
Days on feed 
Weight of animal at beginning of feed 
(pounds) 
800 
900 
1,000 
1,100 
60 ... . 
21.5 
18.4 
15.3 
12.2 
9.1 
23.0 
19.9 
16.8 
13.-7 
10.6 
24.5 
21.4 
18.3 
15.2 
12.1 
26.0 
120 
23.0 
180. ' 
19.8 
240 
16.7 
300 
13.6 
The values given in Table 10 were calculated from the net regres- 
sion coefficients of Table 9. These coefficients were combined in a 
single regression equation as follows : T 
Input of grain per day= 12.5 — 1.55 ( 
days on feed\ 
30 ) 
+ 1.51 i 
fed per day. 
^initial weight of animals 
"Too 
) +0.005 (pound of roughage 
"> The first term of the regression equation, 12.5, in this case, is obtained as follows: 
Xi = 6l2.34X2+&l3.24l3+&14 . . 
xi being the deviation from the average for the dependent variable, t%, X3, and Xi deviations from the 
averages for the independent variables, and 612.34, 613.24. 614.23 the coefficients of net regression. 
Letting Xi stand for values of the dependent variable, X2, X3, and Xi for values of the independent 
variables; and A\, At, As, A\ for the average value of each variable, the foregoing equation can be written: 
A',-.4 1 = 6,2.34(V:2--42)+5 1 3.24(X3--43)+6l4.2c(X4-.4 4 ) 
Or A'l- .ll =6i2.34 A"2 — 6l2. 34^42+6l3. 24 X% — 6l3. 24 -I3+614. 23 Xi~ 614. 23-4 4 
transposing A7i = [^li— 612.34 -42— 613.24^3— 6k. 23^41+612.34 AT2-f-6i3. 24 A"3+6u. 23 Xi 
The terms inclosed by the bracket, composed only of the averages and the net regression coefficients, 
are constant; hence the sum of all those terms is used as a constant "a" in estimating values of ii, for 
given values of the other variables, the final equation reading: 
Al=a-r-6l2.34-Xr2+6'3 24A"3-r-&H.23-X'4 
This is the form of the equation in the text. 
