How can I accurately set up a tri-quadratic equation for curve fitting in Excel?

[mattskie]

Hey,

So I am trying to do a tri-quadratic curve fit (linear regression) in excel. I have successfully completed a bi-quadratic, and it is of the form:
x+x^2+y+y^2+x*y+b (b is calculated by LINEST in excel)

My attempt at a tri-linear was:
x^2+x*y+x*z+y^2+y*z+z^2+b (b is calculated by LINEST in excel)

This equation was fairly accurate for my first few data points in the 4-curve family of curves I am attempting to curve fit, but after that the accuracy plummets.

I am assuming I am on the right track with this, as I attained some initial accuracy, but this equation isn't 100% because I can see it failing. Any/all help appreciated.

Note: I attempted to use the equation on http://www.rmi.ge/~kade/LecturesT.Kadeishvili/MathEconomics/Term3/Week3QuadraticLEC.pdf
but it gave an extremely erroneous solution.

 

[mathman]

Shouldn't the fitting curve be:
ax^2 + by^2 + cz^2 + etc.?