\ \ V] Introduction cxxvii 



If p be the r<n -rclat luii, ^i, ^ the stund.-ird drvi.-itiun.s in the parent population 



and /t'j tin- iv^ivssion o.rtlicient in the s.-iinpl.-, tin? distribution !' A'i ih gm-n by 



n - 3) <V 



jl + j^gp 



where #1= Mean RI = p ^ , the value of the regression in the parent population, 



. Deviation of Ri from Ri 

 and a' = - 



Standard Deviation ot lii 



n being the size of the sample. 

 The requisite transformation is 



x'*/(n-3) = X /(l-x) or 7 

 Thus if x' = 2, we have 



4 4 



x = 7 - = - - =m our case l = '12o. 



We have accordingly to compute 



The value will be found in the column for 71 = 31, or \(ii 1)= 15, between the 

 values of '12 and '13 of #. We have 



KO = '973,9461, S a wo = - 10529, S 4 w = 

 MI =-978,6801, 8 a M! = - 8559, S 4 Ml = 



We are therefore at a part of the table where it is requisite to use S 4 's as well 

 as S 2 's, if we desire an accurate value of P^. Now 



B = -5, <j> = -5, <?</> = -041,6667, 

 and UB = I (-973,9461 + -978,6801) + -041,6667 x 1*5 (-001,9088) 



- -041,6667 x 1125 x 2-5 (-000,0913) 

 = -976,3131 + -000,1193 - -000,0011 

 = -976,4313. 



Hence -952,8626 is the chance that the regression coefficient will lie within 

 twice its standard deviation from the true value in the parent population. 



