Applied Statistics and Probability for Engineers

12-9

In general, we have at the kth iteration

where

This iterative process continues until convergence, that is, until

where is some small number, say, 1.0 

10 ^6. At each iteration the residual sum of squares

should be evaluated to ensure that a reduction in its value has been obtained. This

scheme is available in many software packages. The SAS procedure is PROC NLIN. There

are also several widely used variations of this procedure. For details and examples refer to

Montgomery, Peck, and Vining (2001) and Myers (1990).

L 1 ˆk 2

01 ˆj,k 1 ˆjk (^2) ˆjk 0 , j1, 2,p, p
ˆk 3  1 k,  2 k,p, pk 4 ¿
fk 3 fk 1 , fk 2 ,p, fkn 4 ¿
Zk 3 Zkij 4
ˆk 1 Z¿kZk 2 ^1 Z¿k 1 yfk 2
ˆk 1 ˆkˆk
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