16 
BULLETIN 12M, U. S. DEPARTMENT OF AGRICULTURE. 
areas. Consider the effect on R when w and d are added to y and p. 
In group 7, R is raised from .75 to .84; in group 10, R is increased 
from .80 to .86; and in combined groups 37, 42, and 44, R is in- 
creased from .85 to .90. If quantitative measurements for all 
the other productivity factors were available it is highly probable 
that the correlation coefficients between value per acre and all of 
these factors would be considerably higher than the coefficients 
already obtained between value per acre and a part of these factors. 
The county average values as estimated by the Census Bureau 
appear, therefore, to be highly accurate. 
ACCURACY OF CASH-RENT DATA. 
As stated above, there are two questions relating to the accuracy 
for the purpose in hand of average cash rents, First, do average 
cash rents reflect the average income imputed to land by buyers 
and sellers ? Second, are there enough cash-rented farms to establish 
reliable averages, assuming that they do reflect the income imputed 
to land by purchasers. The first of these questions will be con- 
sidered fully on pages 47 to 53, the second will be dealt with here. 
Since the average cash rents are averages of rents actually paid, 
there is no question of a bias in estimates, as there was in the case 
of land values. But to test their accuracy it must be considered 
whether or not they reflect variations in productivity from county 
to county. To test this, the average adjusted cash rents 9 were 
correlated with the same productivity factors with which land values 
were correlated, and, as in the case of land values, the adjusted rents 
were first correlated with the yield index and percentage of improved 
land. The correlation coefficients between rent and these two vari- 
ables are shown in Table 4. The coefficients between value per 
acre and these two factors are repeated in this table to facilitate 
comparison. 
Table 4. — Cojnparison of the correlation between average rents and productivity 
with the correlation between average value and productivity. 
Croup. 
Number 
of counties. 
Correlation coefficient. 
-Ra.yp. 
-Rv.yp. 
7 .. 
36 
111 
35 
27 
108 
65 
.65 
.81 
.73 
.79 
.70 
.85 
1(1 
.80 
11 
.89 
14 
.89 
32, 33, 37, 41, 42, 44 and 45 
.87 
37, 42, and 44 
.85 
In the combined groups 37, 42, and 44, the correlation between 
adjusted rent and these two productivity factors is the same as the 
correlation between value per acre and these factors, and in group 10 
there is only a difference of 1 point between them. In all the other 
groups the correlation between rent and productivity is lower. But 
in every case the correlation is surprisingly high, considering the 
small number of farms in most of the counties on which the average 
» See p. 6. 
