16 BULLETIN 13822, U. S. DEPARTMENT OF AGRICULTURE 
A more marked correlation is shown between variations of rent and 
price than between those of rent and yield. This is consistent with 
similar indications shown earlier in terms of trends. 
TABLE 6.—I/udexes cf correlation between primary net rent and seven owner- 
Ship factors, 1896-1920 
Gross correlation 2 Net correlation 3 
Factors ! 
Coeffi- | Probable} Coeffi- |} Probable 
cient 4 error 5 cient 4 error 5 
Primary net rent with— 
Brice of: wheatyperioushel 322 22s ee ee ne +0. 44 0.11 +0. 57 0. 09 
Physical: yieldtotiwheat}. = 225-4 ewer eee +. 26 13 +. 47 ealid: 
MIViG;SClECEEGIGOStStSt sett vey cei: UES Meta Sener Pun —.06 ~ 18) +. 28 an OA 
Real-estatel ammate sj eB ee ee —.03 S118) +. 40 11 
Real-estate Vaxcraeee eee.” 14 te RE eT re eA —.11 S18 +. 01 -13 
IReal-estatewaliationesss c=. 2 Se aah e ee Dae ae eee —.14 -13 +.14 5183 
Real-estate increments. £9 Ss RR ae Ie Seay se Es) el a CE = 02 1 Se eae eee oe eee 
1 Per-acre basis, except where otherwise stated. 
2 Simple correlations without allowances mentioned in footnote 3. 
“: 3 Allowances are made for cross correlations among the three factors grouped together by the horizontal 
ines. 
4 Pearsonian coefficient of correlation of deviations expressed in the case of each year as a percentage of 
its ordinate of trend. 
5 Probable error is shown here for the convenience of those who do not agree with the contention that 
the mathematical theory of probability is inapplicable to consecutive items of a statistical time series. 
(Journal of the American Statistical Association, Vol. XIX, March, 1924, p. 7.) ° 
ANTICIPATIONS OF THE FUTURE BY OWNERS 
The net rents received currently in all but five of the years were 
too small to pay a rate on the market valuation of these farms equal 
to that which one might have received on first mortgage loans made 
directly on similar farms in the same couey: 
In other words, a valuation computed by capitalizing rents at 
current rates of interest is less than market ‘valuation during four- 
fifths of the quarter century. Except for the years, 1915-1917, the 
amount of the excess of the computed valuation over the market 
valuation was progressively larger each year beginning with 1909. 
In this real estate there was either a growth of ‘valuation elements 
not included in the computations or else future expectations of 
reduced interest rates or of increased rents were having an enlarging 
influence in the determination of the purchase price. 
It is possible that both kinds of influence were at work in the 
present case. It is desirable to render to each of the types of influ- 
ence its fair share of responsibility, but it is very difficult to do so. 
It is necessary, first of all, to examine the formulas used in the com- 
putations. ++ 
11 Formulas of interrelation of (1) valuation of productive real estate, (2) rate of 
capitalization, (3) net annual rental production, and (4) annual amount of increase or 
decrease of net annual rental production assumed for the future: 
Let v = valuation of productive real estate. 
r = rate of capitalization. 
a= net rental production of real estate in specified year. 
c annual amount of change in a expected in subsequent years. 
The formulas follow: 
c 
Solving for yaluation, v=s+5: 
32 4ey 
Solving for rate of capitalization, pa ask Var racy 
Solving for anticipation of rental changes, c=—r (yr — a). ‘ 
spas c 
Solving for present capitalizated value of anticipated rental changes, iL. aS 
