KiRSTiNE Smith 
11 
when 
aoMo + ai9«i + agmg + + ct„m„ = 1 
aoMi + a^mg + a^nis + + a„H?„+i = x 
ttomg + al??^3 + a^ni^ + + a„?H-„+2 = 
.(16). 
Let be another adjusted value, then 
ys = ^S [yo + 71 + 723^' + + 7«^"]| . 
where 
7o™o + 7i™i + 72 '"'2 + + r«"'« = 1 ^ 
70™1 + 7lW^2 +72'% + + Yn^^^n+l = 
70^2 + 71^3 + 72W''4 + + 7«"^n+2 = 
.(17). 
Hence the condition that y,. and ?/s are uncorrelated is, since the squared standard 
deviation of the observed y^, equals a^f(Xp), 
S K + o-iXp + a.^x',+ + a„x\]] . [yo + yiX^ + y^xl + +7na?"]| = 0, 
or S IjI^^ [ao + a^Xj, + a^x; + + a^xl] 
+ S 
r I 2.3, , n + 11 
[aoXj, + a^x,, + ttga;^, + + a„x^, J 
+ ^ \f^) t"o^'' + + 4 + + o.nxl'^-] 
v 
Yn 
+ '5 ^jj^ ^ [o.qxI + a-^xl^'' + a^xl'^- + + a„a;',"]|- = 0. 
Remembering that *S , » , , 
= Nm,q and applying the relations (16) this re- 
duces to 
7o + YiXr + 72^;'' + + YnXy = 0, 
from which the 7's are ehminated by (17). 
0 1 
1 JWq 
Xf. mi m, 
X, m„ m 
.. 
.... TO„ 
TO3 .. 

m4 . . 
— m„_,_2 
w '"■n+1 '^''m+2 
= 0 
.(18) 
is therefore the condition that and ?/s are uncorrelated. 
