350 
On Linearity of Regression 
(ii) For more exact work , ^ should be calculated from the formulae 
•67449-2 ^•VrT(r^T)^-(l-r^y' 
E^ -67449 "2 ^ ' 77 + r _^ r(l - t?-)^ - 77 (1 - r^)^ 
77 +r 
Each of these results gives an approximate formula for the same physical 
quantity (i.e. the number to be looked up in the table of the probability integral if 
we want the probability in favour of the distribution being linear). 
If these ratios work out sufficiently nearly equal this constitutes some justifi- 
cation for the statistical approximations made in obtaining the formulae, but if 
on comparing the values of the ratios the agreement is unsatisfactory, and 
no mistake in the arithmetic can be detected, then the probable errors of E^, E^ 
must be calculated from the complete formulae (xxii), (xxvi), (xxviii) in terms of 
the subsidiary quantity ■rs and substituting for S,,^ its value as determined by the 
complete formula given by Karl Pearson. 
