382 
BANKING STANDARDS 
probable error squared for unit weight is taken as equal to o.1. 
The weighted mean value of E. is thus —- 0.46 + 0.05. 
In a similar manner, the weighted mean value of K, was deter- 
mined to be + 1.39 = 0.16. 
Substituting the above two values in (1), there is obtained 
+1.39—0.46 (AT)= AN... ....(8) 
which is an expression superior to (6) because in (6) the groups 
are weighted according to their respective number of banks, 
whereas in (8) the weighting of each constant is inversely as its 
own probable error squared. Hence, using (8) and (7), the 
best obtainable general measure, for any bank in this district 
picked at random, of the relative influence of the annual changes 
in gross earnings and in total expense upon net earnings is 
=) 1.67. That is, generally speaking, gross earnings are 
4 
57% more important than total expense in determining net 
earnings. 
TaBLE VI 
CoMPUTATION OF BEST GENERAL VALUE oF E’,, THE COEFFICIENT 
ExprRrRESSING THE M0ST GENERAL EFFECT OF A CHANGE IN TOTAL 
ExPENSE RaTios oN A CHANGE IN NET EARNINGS RATIOS 
Groun* 
Probable 
Error 
+=0.08 
+0.09 
0.10 
= MN 
(Probable 
Error)? 
0.00064 
0.0081 
0.0100 
0.0144 
Value of E'¢ 
—0.40 
—0.30 
—0.62 
—0.33 
Weight 
15.6 
12.4 
10.0 
8 
Product, 
Weight X 
Probable 
Error 
—7.644 
—~4.836 
—6. 200 
2.739 
Ses Table I of Appendix I. . . ] 
Sum of products = —21.419; sum of weights =46.3; weighted mean = —o.46; probable error of weighted 
mean = =#%0.0%. 
GRAPHICAL REPRESENTATION OF RELATIVE EFFECTS OF CHANGES OF 
GROSS EARNINGS AND OF TOTAL EXPENSE RATIOS 
ON NET EARNINGS RATIOS 
In Chart I are shown the various regression lines, plotted with 
net earnings as ordinates and gross earnings and total expense 
as abscissae. The equation of each line is shown immediately