GROSS EARNINGS IN DISTRICT I 279
between gross earnings ratios and those of total expense and of
net earnings, is to select for the respective series suitable averages
 with which the ratios in the correlated series may be compared.
 Those chosen are the yearly averages of the banks in
the various volume (earning assets) groups.
Having selected standards of reference for the series to be
correlated, as for instance gross earnings and total expense, the
process of manipulating the data is as follows: (1) For each
volume group, determine the percentage amounts and directions
by which the ratios in the correlated series for each of the banks
in 1924 deviate from the 1924 group average. (2) Select classes
of uniform widths into which are placed the paired variables
(deviations) for each bank, the resulting distribution being of
the double-frequency type. (3) Repeat this process for each
of the volume (earning assets) groups and combine the frequencies,
 thus securing a distribution for all banks in the year
1924. (4) Repeat processes (1) to (3) for the year 1925. (5)
Combine the distributions for the two years.
The frequencies in Table 159 show the results of carrying out
these steps for paired ratios of gross earnings and of total
expense to earning assets, and supply the bases for the summaries
 at the right and at the bottom of the table. These are
obtained as follows: (1) total the number of instances in the
respective lines and columns; (2) add and then average the
amounts in each line so as to get the average percentage dispersion
 for the factor in the stub, used as the independent variable;
(3) algebraically add and then average the amounts in each
line so as to get the net average percentage deviation for the
factor in the caption treated as the dependent variable, and (4)
reverse processes (2) and (3) so as to get the average percentage
dispersion of the factor in the caption when used as the independent
 variable, and the net average percentage dispersion for the
factor in the stub when treated as the dependent variable. The
results of steps (2) and (3) supply measures of regression of total
expense on gross earnings; those of step (4) measures of regression
 of gross earnings on total expense.
Similar analysis was made of the relations between ratios
of gross and of net earnings, the results of carrying through the
processes for the two paired series being summarized in
Table 160.