ccxlvi Tables for Statisticians and Biometricians [LII LIP** 



Accordingly since u Q (d) = 725,3521, 



ff = (u (0) - w ) Aw = '068,4659, 

 | ff (I -6') = '0318,8916 



and = -068,4659 + -0318,8916 x 



= -075,0163. 

 Thus p = -5 + 9 = -5750, 



and this is the best value at present available for the multiple correlation in the 

 parent population. 



Illustration (iv). Suppose p = -3, ^=315 and n = 5. We require JR* and o-tf. 



This is about as unfavourable an example as we can call upon the Tables to 

 supply the answer to. 



Consider: log 25 = log 25 -f x log 2, 



log 50 = log 25 + 1 x log 2, 

 Iogl00 = log25 + 2xlog2, 

 log 200 = log 25 + 3 x log 2, 

 log 400 = log 25 + 4 x log 2. 



We need log 315 = log 25 + - log 2 



= log 25 + 3-655,3516 log 2. 



Now write down the y, values for 25, 50, 100, 200, 400 from Table LII in 

 inverse order and difference them. We find : 



u Au A 2 A :f w A*u 



400 -908,1271, 



200 -906,2394, --001,8877, 



100 -902,4191, --003,8203, -'001,9326, 



50 -894,5964, -'007,8227, -'004,0024, -'002,0698, 



25 -878,1999, -'016,3965, --008,5738, -'004,5714, -'002,5016. 



The differences are thus slightly diverging but the forward difference formula 

 will suffice. 



We have = 4 - 3'655,3516 = -344,6484 and accordingly : 



u e = -908,1271 - -344,6484 x -001,8877 + -112,9329 x "001,9326 

 - '062,3146 x '002,0698 + '041,3668 x '002,5016 

 = -908,1271 - '000,6506 + '000,2183 - -000,1290 + '000,1035. 



Clearly the required value is greater than '907,5658 and less than '907,6693. Taking 

 it equal to the mean of these we have: 71 = '907,6175. Hence by formula (i): 



jp= i _||o x -907,6175 = -101,0817. 



