248 HARRIS: RELATIONSHIP OF OVULES TO SEEDS 
Constant Series of 6,000 Pods Series of 10,000 Pods 
Coefficient of correlation, 7... 6.0.0. .006. 5673 =.0059 .6133 =.0042 
Corelation fatios fel is ea .5677 =.0059 .6140 +.0038 
EU CTEMOR FAS Vw a uk -00035 
wyatt stat Misty Jr eatery wy Ups Rabe man AL Par ae .00040 -00081 
Note the exceedingly small differences between r and y. Fora 
scientific test of linearity, we have recourse to the constant ¢ as 
suggested by Blakeman,* 1. e.: 
VN pa 
-3V5<2 
67449? ? 
which gives 
HOP: 0,000 D008 2604p oy oh dis os Was sews oles ¢/Eg = 1.144 
HGP, EO\000 pods ot awe copa cu ete ait eo int a iene &/Eg = 2.110 
Hence regression may be considered linear within the limits of the 
probable errors of random sampling. 
The reason so much stress has been laid upon the question of 
the nature of regression is two-fold. First, the validity of the 
correlation coefficient as a description of the relationship between 
the number of ovules formed and the number of seeds developing 
depends upon linearity of regression. Second, it is a matter of 
considerable biological importance to know that the rate of change 
in the number of seeds developing per pod remains constant from 
one end of the range of variation of number of ovules per pod to 
the other. 
The coefficient which measures the relationships between the 
number of ovules per pod and the capacity of the pod for maturing 
its seeds is not 7, but 7,2. The results are: 
Pot the frst 6,000.5 05s) a eee Tor = — .0714 =.0087 © 
For the additional 4,000.03 scl ais ts Yor = — .0358 =.0106 
For the whole: 10,000. 0 60... ea Yor = — .0597 +.0067 
The first and third constants are clearly significant statistically 
deviating from o by about 8 or 9 times their probable errors: the 
second constant may also be significant but it differs from 0 by 
only about 3.5 times its probable error. They indicate that the 
pods with the larger number of ovules are not as capable of matur- 
* Biometrika 4: 332-350. 1905. 
