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. Equa- 
tions 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 earn- 
ings lines is easily contrasted with the variation in slopes of the 
total expense lines, which are also easily compared and con- 
trasted with each other. (Note, for example, the large difference 
in slope of lines@ and @.) The regression lines also show a rela- 
tion 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 in- 
crease, 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 equa- 
tions (1) and (2). 
Group 1. In this group both constants, K, and K,, in the re- 
gression 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-