446 



THE AMERICAN NATURALIST [Vol. XLIX 



even more conspicuous. The correlation for per cent, ni- 

 trogen is r = . 115 + .044 as compared with r=.603 + .029 

 for weight of grain produced. 



This point will not be discussed in greater detail here, 

 since the problem of the relative susceptibility of various 

 characteristics of the individual to environmental influ- 

 ence has been the subject of experimental and statistical 

 studies which have been under way for several years and 

 will probably eventually be published. 



III. On the Nature of the Regression of Associated 

 Plots 



The correlation coefficient is strictly valid as a measure 

 of interdependence only when regression is linear, i. e., 

 when the means of the second variable associated with 

 successive grades of the first lie in a sensibly straight line. 

 The equation for the regression straight line 



V% - ( Vt ~ r PlP . z Jh ) + r PlPt ^ pi 



for the second on the first ultimate plot of the same com- 

 bination plot reduces to 



p—(p — rp) + rp, 



when symmetrical tables in which p l = p 2 , a Pl = <r fi are 

 used. 



The testing of the linearity of regression in any indi- 

 vidual case is rendered somewhat difficult by the necessity 



• EOTHAMSTED WHEAT EXPERIMENT 



