A question about capabilities of linest function

[Jim Dukelow <jsdukelow yahoo com>]

I am using linest to attempt a polynomial fit in two numeric variables 
and two categorical variables (for which I have assigned +1 and -1 proxy 
values).  The fit I am shooting for is up to fourth power in the 
numerical variables and 1st power in the categorical variables, with 
cross-terms.  I have columns for the observed values of L, L^2, L^3, L4, 
F, F^2, F^3, F^4, L*F, (L^2)*F, etc., L*T, (L^2)*T, etc., F*R, etc.  -- 
42 terms in all.  The observed values of my dependent variable are in 
the vector b8:b349.  The observed values of my dependent variable have 
up to 10 significant figures.  The observed values of the independent 
variables have one or two significant digits in the measured first 
powers (the original data) and up to 8 or 9 significant digits in the 
higher powers.

Values of L and F are normalized to live between -1 and +1.

I marked an array 5 rows by 42 columns, entered the command

linest(b8:b349,f8:au349,true,true),  and  held down  CTRL-SHIFT-ENTER.

More of less instantaneously, the array was filled with  #NUM  error 
messages  and my command was now

{=linest(b8:b349,f8:au349,TRUE,TRUE)}(42,5)[0][0]

The Help pages are not much help in telling me what has gone wrong.

I recognize that using successive powers of  L  and  F, rather than 
orthogonal polynomials, may lead to ill-conditioning of the 
calculation.  Am I simply asking  linest to do more than it is able, or 
is my problem elsewhere.  Should I take this problem to R or Maxima or 
Octave?

I would appreciate any help you can provide.

Jim Dukelow