578 



Journal of Agricultural Research 



Vol. XX, No. 7 



By substitution of the correlations in these formulae the following 

 results are obtained: 



4>(BWRT) = 0.4002 

 <t>{BWR) = .6884 

 4>{BWT) = .5665 

 4>(BRT) = .4668 

 cj>(WRT) = .7788 



4>(BW) = 0.9216 

 <£(£#) = .7696 

 cj>(BT) = .6519 



0(PFi?) = 0.9999 

 <j>(WT)= .9996 

 <K#T) = .7791 



These give values of the coefficients of determination identical with 

 those given by the indirect method. 



This method, as was shown in part I, is essentially the same as Pear- 

 son's method of calculating multiple regression. 



Let A = 



Let 



A BB = A with column B, row B, deleted. 



Abb 588 0.7788, A BK = 0.2028, A BT = 0.3687, A BW = 0.2275 



A BW - A 



pB-vr=T— =0.2921 



P =~ 



rB-R ^ 



-—=0.5139 



0.2604 



Abt 

 /'b-t = T- =0.4735. 

 -*bb 



These values are identical with those obtained by the preceding 

 methods. 



It will be seen that the first method, while apparently less direct than the 

 others, is really less laborious. The solution of three simultaneous equa- 

 tions requires merely the evaluation of a determinant of the third order 

 instead of one of the fourth order, as in the last method. The expression 

 <j>(BWRT) in the second method is, of course, merely an expansion of 

 the same determinant of the fourth order as that used in the last. The 

 indirect method, moreover, gives more insight into the processes followed 

 than the others in which there is a substitution in what appear to be 

 arbitrary formulae. In line with this last point, the indirect method is 

 more flexible in that it can be used to test out the consequences of any 

 assumed relation among the factors. 



ANALYSIS OF CAUSAL RELATIONS 



In attempting to interpret the present results in terms of causation, 

 we see at once that the scheme of relations chosen is not a very satis- 

 factory one. The wet-bulb depression was measured under shelter. Con- 

 sequently the coefficient of determination, d B<E = 0.0678, can not measure 



