RELATION OF LAND INCOME TO LAND VALUE. 
i:> 
The problem then is to find the correlation between average value 
per acre and these productivity factors. 
Let v = average value of land per acre. 
a = average cash rent per acre. 
y = average yield per acre. 7 
p = percentage of improved land. 
w = percentage of woodland. 
d = percentage of land needing drainage. 
The problem of finding the correlation between v and the rest 
of the productivity factors combined is a problem in multiple corre- 
lation. 8 When there is a perfect correlation of v with y, p, w, and d 
combined, the coefficient of correlation (R VmVpw d) will be 4-1. If 
there is no correlation R v . VP wd will be 0. Perfect correlation is 
practically never found in dealing with economic data, but coefficients 
of .80 or .90 may be regarded as very high. 
Since it may be true that some of these productivity factors may 
not be of much importance or may be nearly constant from county 
to county, the correlation of v with y and p combined was first deter- 
mined. These correlation coefficients are shown in Table 3. 
Table 3. — Coefficients of correlation of value of land per acre with yield and per- 
centage of improved land. 
Group. 
Number of 
counties. 
Rv.yp. 
7 
36 
111 
35 
27 
108 
65 
0.75 
10 
.80 
11 
.89 
13 
.89 
32, 33, 37, 41, 42, 44, and 45 
.87 
37,42,44 
.85 
The correlation coefficient for each of these groups is remarkably 
high, considering the number of excluded productivity factors for 
which there are no quantitative measurements. The highest cor- 
relation between value and these two productivity factors is found 
in groups 11 and 13, the lowest in groups 7 and 10. Because of the 
important influence on land values oi the excluded productivity 
factors, it can not be concluded, however, that the census estimated 
land values are less accurate in groups 7 and 10 than in groups 11 
and 13. It is more likely that R is higher in the latter areas be- 
cause some of these factors, such as distance to central market, 
percentage of land needing drainage, and mileage of good roads, 
are more nearly constant from county to county than in the former 
V Since yields of crops vary so much from county to county for any given year, because of geographical 
variations in rainfall, average yields were not computed from census data. Instead a 10-year average yield 
for corn, oats, wheat, and hay was obtained from the Crop Reporting Board of the Bureau of Agricultural 
Economics. From these averages an index of yield was obtained for each county. This was done by ex- 
pressing each county average yield for each crop as a percentage of the group average yield. The yield of 
corn, for instance, in a county in group 10 was expressed as a percentage of the average yield of 
corn for group 10. These relative yields for each of the crops were then summed and divided by 4, thus 
giving a yieldindex. A 10-year average yield was not available for cotton, so that it was necessary t o work 
out the yield index for the southern groups on the basis of the 1 year crops alone as reported in t he last 
census. This index is based upon the yields of cotton and corn and was obtained by the method outlined 
above, except the county average yields were expressed as percent ages of the average yield of all the southern 
groups mentioned, rather than as a percentage of the group average in which t he count y was located. This 
was done because all these groups were thrown together for this correlation study. 
8 For a discussion of partial and multiple correlation see Yule, Introduction to the Theory of Stat istics, 
Ch. XII. 
