This is a very interesting way to multivariable and multipower regression. I am following cummings54 logic with the powers, I think. For instance
B1:B10^{1,2,3,0,0,0,1,2,3}*C1:C10^{0,0,0,1,2,3,1,1,1}
Call "x" the B column, and "z" the C column. This above form will give you the coefficients for an equation of form:
Y=a1*(x^1)*(z^0)+a2*(x^2)*(z^0)+a3*(x^3)*(z^0)+
a4*(x^0)*(z^1)+a5*(x^0)*(z^2)+a6*(x^0)*(z^3)+
a7*(x^1)*(z^1)+a8*(x^2)*(z^1)+a9*(x^3)*(z^1)+a10
where I am looking for a1, a2,...,a10. To get Excel to give me this coefficients a1, etc. I select cells 1 row by 10 columns (1 for each coefficient I want to output), type in
=LINEST(Y1:Y10,B1:B10^{1,2,3,0,0,0,1,2,3}*C1:C10^{0,0,0,1,2,3,1,1,1},TRUE,TRUE)
in the fx (function) box at the top, then hit CTRL-SHIFT-ENTER to get Excel to do the curve fitting for those coefficients. What I don't understand is the logic Excel uses for the output; in my 1 row by 10 column block of cells, where do the a1, a2, etc. go? Looks like 'a10', the constant term, always goes at the end. But it seems like it reverses the sequence of (remember, column B is x, C is z):
x^{1,2,3,0,0,0,1,2,3}*z^{0,0,0,1,2,3,1,1,1} so that the powers are reversed and the x and z are reversed. I will guess:
column coefficient
1 a9
2 a8
3 a7
4 a6
5 a5
6 a4
7 a3
8 a2
9 a1
10 a10 (the constant)
this doesn't seem to be the correct output sequence. I tried, for instance, just using only one term (say a2*x^2, plus the constant a10) to compute a sequence of 'Y', then curve fitting with =LINEST(Y,x^{1,2,3,0,0,0,1,2,3}*z^{0,0,0,1,2,3,1,1,1},TRUE,TRUE)
and the non zero coefficient kept jumping around in that 1x10 block I've selected in the worksheet.
,LN(x),,),1,2))