374

BANKING STANDARDS

net earnings for banks in which total expense did not change, from
1924 to 1925, in units of o.1 point;
+X. is a constant representing the average amount of increase in
net earnings for banks in which gross earnings did not change, from
[924 to 1925, in units of o.1 point;
+E’; is a coefficient expressing the effect of a change in total expense
 ( AT) on a change in net earnings (AN);
+E’, is a coefficient expressing the effect of a change in gross earnings
 (AG) on a change in net earnings (AN);
pis a residual. It represents the discrepancy between the observed
change in net earnings and (1) that computed from the observed
change in total expense alone (from equation (1) ); or (2) that computed
 from the gross earnings alone (from equation (2) ).

Otherwise stated, equations (1) and (2) are merely the equations
 of the regression lines, respectively, of the annual change
in net earnings on the annual change in total expense, and of the
annual change in net earnings on the annual change in gross earnings,
 the origin of each line being the point of zero change in net
earnings and in the other two variables.
The assumed constants, K,, K,, E,” and E/, were derived by
the method of least-squares. The probable errors of these quantities
 were, in each case, computed rigorously from the normal
equations, and the residuals, v, of the substitution in the observation
 equations.
TaBreE I

Groups AND NUMBERS OF MEMBER BANKS, BosToN FEDERAL RESERVE
DistrIiCcT, RELATIVE TO AVERAGE GROSS EARNINGS
AND TotAL EXPENSE RATIOS, 1024

RATIOS: GROSS EARNINGS
TO EARNING ASSETS,
ABOVE OR BELOW THE 1924
AVERAGE OF 6.0%,

Above

Below

Ratios: Total EXPENSE TO EARNING ASSETS
ABOVE OR BELOW THE 1024 AVERAGE OF
4.29%

Group 1
Number of banks, 129
Group 4 | Group 2
Number of banks, 83 Number of banks, 132

ABOVE

BerLow
Group 3
Number of banks, 64

For purposes of analysis, the 408 member banks were divided
into four groups according to the amounts of the gross earnings
and of the total expense ratios in 1924 relative to the average
gross earnings (6.0%) and the average total expense (4.2%) in