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 distribution
 approaches the normal law of error, the closer the agreement
 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 knowledge
 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