A Cubic regression to a number of points (2 independent variables!)

Hi All,

I posted this question to the pre-university problem a few days ago, but it seems nobody can answer, so I will try my luck here.

I want to approximate a surface with a cubic regression in the following form. (Where X is the temperature, Y time and and z the energy requirement: Thus f(x,y)=z.)

a⋅x^3+b⋅x^3+c⋅x^2⋅y^2+d⋅x^2⋅y+e⋅x⋅y^2+f⋅x^2+g⋅ y^2+ h⋅x⋅y+i⋅x+j⋅y+k

However I am not sure if I wrote correctly the cubic equation???

If somebody could tell me wherever it is correct or not. And if not, what is wrong :-)

a,b,c,d,...etc. are the coefficients.

By the way, what is the general form of such two variables dependent quadratic or cubic equations?

Thanks a lot in advance.

Cheers,

Martin http://www.mathhelpforum.com/math-he...c/progress.gif http://www.mathhelpforum.com/math-he...ttons/edit.gif