378 
BANKING STANDARDS 
—o0.040+0.767 (AG)= AN....... 
+=0.12 =£0.02 
cee) 
The probable errors of the constants K, and E./, + o.12 and 
+ 0.02, respectively, were computed rigorously, as in the case of 
total expense, from the normal equations and the residuals, v, of 
the 408 observation equations. The constant — 0.040 = 0.12 has 
no significance in this case because it is 14 its own probable 
error. The interpretation of (7), therefore, is, that the most 
probable effect of a change of, say, 1 (0.1 of a point) in gross 
earnings from one year to the next is to change net earnings 
0.767 (0.0767 of a point) in the same direction. 
From (7) and (6), therefore, one can obtain at once an ap- 
proximate measure of the relative influence of a change in gross 
earnings and of a change in total expense on a change in net earn- 
ings; that is, their respective importance is as 0.767 is to 0.497, 
or a change in gross earnings is (1 =— 1.54), 54% more in- 
fluential on net earnings than total expense. 
But this result (54%) is not the best obtainable because it 
has been shown in Table II that if one assumes gross earnings 
to influence net earnings equally in all groups, total expense does 
not influence net earnings equally in all groups. The evidence 
from Solution S;, which produced equation (7), is given in Table 
III, from which the mean v column, especially, shows that if it 
is assumed that total expense influences net earnings equally in 
all groups, gross earnings influences it unequally, particularly 
in Groups 3 and 4. The interpretation of the mean v in Group 
3, + 1.2 4 0.3, is that (bearing in mind the above assumption) 
TasLE III 
RESIDUALS OF SOLUTION S, 
1 
Grour* 
Total 
I 
~ 
a 
Sou oF 
+e 
+exz 
+182 
™ 
~o 
tree 
tran 
" 
“n 
+30 | — 
4-0 
NuMBER 0% 
- . 
MEeaN 
v 
rr 
+o. 
4 
_- 
+- 
40 | —1.0 =0.3 
” 
Number 
OF 
Banks 
To? 
MEAN 
nd 
ProsB- 
ABLE 
Error 
4" 
8 *5.2 
— — 
1079 2 __*34 
| 1322 21 | ®7.9 
oT 7 Is *3.6 
260 
#See Table I of Appendix I.