APPENDIX 1

383

beneath the figure, each line being numbered the same as its
equation and the same as the group to which it pertains. Equations
 and lines (A) and (B) are the general equations applicable
to all groups. The relative influence of gross earnings and of
total expense on net earnings is readily apparent in the relative
slopes of the paired lines (1) for each group, and (2) for the
combined groups. The uniformity of the slopes of the gross earnings
 lines is easily contrasted with the variation in slopes of the
total expense lines, which are also easily compared and contrasted
 with each other. (Note, for example, the large difference
in slope of lines@ and @.) The regression lines also show a relation
 which is not readily apparent from an inspection of Table IV
—that is, the tendency for the total expense lines to cross the
line of no-change in gross earnings, or total expense ratios above
the origin. The interpretation of this is that, generally speaking,
for banks in which total expense did not change from year to
year, there is a strong constant tendency for net earnings to increase,
 and this increase can be due only to an increase in gross
earnings in those banks. Stated in other words, it means that,
generally speaking, total expense ratios must increase about 0.3
of a point before net earnings will show a decrease; i. e., before
the influence of the increase in gross earnings is counteracted.
Further reference to Chart I will be made subsequently.

CONSTANT REGRESSION TENDENCIES IN NET EARNINGS

The tendency for the three variables here under discussion to
regress to their respective average values has been developed in
Chapter XVII. It is proposed to discuss briefly the constant
tendency for net earnings ratios to regress to their average value,
independently of changes in the other two variables, each of
which is thought of as acting separately, as indicated in equations
 (1) and (2).
Group 1. In this group both constants, K, and K,, in the regression
 equations are without significance. (Note in Chart I that
lines and @ practically pass through the origin.) The amount
of regression, therefore, of net depends almost wholly upon the
changes in gross earnings ratios or total expense ratios. That is,
the constant tendency for net earnings ratios to change is negligi-