488 On Bravais' Formula in the case of Skew Correlation. 



12 ?*23 ?*24 



1 fsi 



^34 1 



and we may again call 



tlie net coefficient of correlation between Xi and # 2 . Expanding the 

 determinants, we have, in fact, 



........ (16). 



There are six such net coefficients, /> 12 , /> 13 , /3 14 , p^ p Ut p u . The 

 above values of the regressions are again those usually obtained on 

 the assumption of normal correlation.* The net correlation p n 

 becomes, on that assumption, the coefficient of correlation for any 

 group of the %i w z variables associated with fixed types of # 3 and # 4 . 

 If we write 



we have, after some rather lengthy reduction, 



where 



1 



4 ) J 



In normal correlation, o-!-/! ^i 2 is the standard deviation of all aj r 

 arrays associated with fixed types of x z , 3 , and # 4 . In general corre- 

 lation, it is most easily interpreted as the standard error made in 

 estimating 0*1, by equation (14), from its associated values of x 2 , # 3 , 

 and x^ 



As in the case of three variables, the quantity R may be considered 

 as a coefficient of correlation. It can range between +1, andean 

 only become unity if the linear relation (14) hold good in each indi- 

 vidual instance. 



We showed at the end of the last section that the standard error 

 made in estimating x 1 from the relation 



*' Professor Pearson, " Eegression, Heredity, and Panmixia." ' Phil. Trans.,' 

 > Yol. 187 (1896), p. 294. 



