376 
BANKING STANDARDS 
and (2) the most probable effect of a change of, say, 1, (0.1 of a 
point) in total expense from one year to the next is to change net 
earnings 0.497, (0.0497 of a point)—neglecting the constant— 
in the opposite direction. 
If total expense were the only thing determining net earnings, 
and if a straight-line equation like (1) represented the law of 
variation perfectly, the residuals, v, would all be zero. The 
smaller the residuals and the more closely their frequency dis- 
tribution approaches the normal law of error, the closer the agree- 
ment between theory and fact. 
While it was not expected that the residuals in (1), applied 
to all 408 banks, would be zero, first, because gross earnings is 
neglected, and second, because of a possible variation from a 
linear relationship, it might be expected, in the absence of knowl- 
edge to the contrary, that the character of the distribution of the 
residuals in Solution 7, would be the same for each of the groups 
of the 408 banks. That is, the most natural supposition would be 
that the law of variation of net earnings, in so far as it depends 
upon total expense alone, is the same for the banks in each of 
the groups in Table I. 
In order to determine whether the influence of total expense 
on net earnings is the same, regardless of the group-location of 
the banks, the residuals of Solution I, were studied in groups, 
as shown in Table II. 
TasrLE II 
RESIDUALS OF SOLUTION [, 
Group! 
mT. - 
Son 
NUMBE® ~® 
WAL 
NUMBER 
OF 
BANks 
Fy2 
‘Te 73 
MEAN 
9 
Proz- 
ABLE 
Error 
+7.0 
*5.7 
*=10.3 
*=6.3 
*See Table I of Appendix 1. 
This table contains very strong evidence—if not proof—that the 
law of variation of net earnings, in terms of total expense, is not 
the same for banks in the different groups, and, if it is assumed 
for the moment—a fact which will be demonstrated later—that