Within limits, you can do it. Help for LINEST is extremely misleading,
it fits general linear models, not just straight lines.
http://www.stfx.ca/people/bliengme/ExcelTips/Polynomial.htm
shows how to fit a polynomial. In general, you just have to pass the X
matrix (less the initial column of 1's for the grand mean). If you
request statistics (TRUE as 4th argument), then the second output line
will be the standard errors of the coefficients (1st line of output).
That will allow you to test significance of any coefficient.
The biggest limit is that larger models can easily become
ill-conditioned. Prior to 2003, LINEST directly solves the normal
equations, instead of doing an SVD on X. The result is that numerical
singularity depends on the condition number of X'X instead of X (i.e.
LINEST would need quad-precision to do some problems that S-Plus and R
can do in double-precision). SAS (other than PROC ORTHOREG) also works
with X'X, but it warns you of numerical singularity instead of charging
ahead and producing nonsense results.
Another limit is that LINEST will not fit more than 17 parameters (the
intercept counts, if requested) even though MINVERSE will attempt to
invert up to a 52x52 X'X matrix.
Jerry
