38s 
ble. Change occurs normally only when either or both gross 
earnings and total expense ratios change. 
APPENDIX I 
Group 2. In this group, the constant, K, = -o0.20, is without 
significance, but the constant, K; = + 2.16 4- 0.27, (see Table 
IV), is significant. For banks in this group, in which total ex- 
pense ratios did not change, there is a strong constant tendency 
for net earnings ratios to increase 0.216 points per year. This 
is presumably due to the regression tendency for gross earnings 
ratios in this group to increase. Moreover, total expense ratios 
must increase as much as (G2=) 5.5 (or 0.55 of a point) 
to offset this. This fact may be seen also from regression line 
@ in Chart I. 
Group 3. For banks in this group, in which gross earnings ratios 
did not change, there is a strong constant tendency for net earn- 
ings ratios to decrease. The amount of the decrease is given by 
the constant K,=—-1.32 + 0.39, which means a decrease of 
0.132 of a point per year. This is presumably due to the regres- 
sion tendency for total expense ratios in this group to increase. 
Moreover, gross earnings ratios must increase as much as 
Goons =) 1.7 (or 0.17 of a point) in such banks to offset this 
tendency. This is shown graphically on Chart I, regression line ®. 
The constant K; == — 0.35 + 0.48 also shows a constant tend- 
ency for net earnings to decrease, but it is without significance 
because of its large probable error. 
Group 4. In this group, both constants, K, = -} 1.02 + 0 20 
and K, = 2.47 + 0.31, are significant in showing a strong 
constant tendency for net earnings ratios to increase from year 
to year, in the first case, for banks in which gross earnings ratios 
did not change; and in the second case, for banks in which total 
expense ratios did not change. In the latter case the tendency is 
the larger. In banks in this group, gross earnings ratios must 
decrease =) 1.3 (or 0.13 of a point) to offset this constant 
tendency for net earnings to increase, and total expense ratios 
must increase as much as Gal=) 7.5 (or o.75 of a point) 
annually to offset it. These facts are shown graphically in Chart 
I by the regression lines ® and @, respectively.