Jan. 3, 1921 



Correlation and Causation 



57i 



For a single cause and effect the required formula is merely d^-r 2 ^ 

 (fig. 10). 



?4 



Fig. 10.— Effect and one known cause. 



The degree of determination by residual factors; that is, a\. , is thus 



1— r 



If two causes are known, and the degree of correlation between them, 

 we have (fig. 11) — 



,4 



p K u.— Effect and two correlated known causes. 



B r XA + B r XO~ X 



\2 



(i-^ 2 xb)(i-»' 2 ab) I-^XB 



r 2 xo = ^x-o = 



I — y XA — r XB ' AB 



i — r 2 



»' 2 x B -»' 2 ab+2»-xa'xb''ab. 



Fig. 12.— Effect and three correlated known causes. 



If three causes and their correlations are known (fig. 12), we have 



cb' 2 xa + cb^xo = 1 . * r° m which 



1 - Zr 2 XA + 2?r XA r AB r» x ~ zSriAWgcTCT + Sr 2 XA r 2 BC . 



r 2 = d = 



' xo — u x-o 



- y 2 AB - r\c - r\c + 2 r AC r CB rv 



