EXPENSES IN DISTRICTS I AND IJ 297 
average for each group in 1922. (3) Add the ratios for 1923 
for the banks falling in each of the groups in 1922, and divide 
by the number of ratios, thus obtaining a 1923 average for 
each group for which a 1922 average is secured. (4) Compare 
the two averages by subtracting the amount for the first from that 
for the second year. In order to cover all years, repeat these 
processes for 1923 and 1924, and 1924 and 1925; total the sums 
of the ratios and of the instances by groups for the three pairs 
of years, compute averages for the combined first years and 
combined second years, and compare the results by subtracting 
the amount for the first from the amount for the second years, 
By carrying through these several steps for member banks in 
the Boston district, the results in Table 170 are secured. They 
give direct and simple measures of regression, expressed in points 
of change in the average ratios between successive years, of the 
same types as those already found for the same body of data, 
but arrived at in other ways. All methods agree in indicating that, 
on the average, total expense ratios which are low in a given year 
tend to increase, and those which are high tend to decrease 
the following year, the amounts of the change, expressed abso- 
lutely or in percentage form, being positively correlated with 
the positions of the ratios on the expense scale. There is re- 
gression to type, the amount being largest for banks in “exposed 
TABLE 170 
AVERAGE NET CHANGE IN RATIOS oF ToTAL EXPENSE TO EARNING 
ASSETS, BY PAIRS OF YEARS, 1922-1925, MEMBER BANKS, 
BosTON FEDERAL RESERVE DISTRICT 
YEARS 
RaT108: Total 
Expense to 
Earning Assets 
First Year of 
Each Pair of 
Years) 
and under 
and under , 
and under «4 
and under : 
; and under 6 
> and under 7 
+ and over 
iumha- 
Total 
Second 
ears less 
_irst 
ton po 
‘IT 6 
1022 and 1022 
Numkbe 
Second 
=a" less 
t 
te “0 
1923 and 1024 
Second 
“»ar less 
irst 
>. 
0.4 
-— 2 
1924 and 102% 
Number 
Second 
=r less 
-st 
- 
ST 
to.x 
-0.3 
-0.2 
-_y A