Is My Tri-Quadratic Curve Fit Equation Accurate Enough?

[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.Ka...adraticLEC.pdf
but it gave an extremely erroneous solution.

 

[Stephen Tashi]

You should describe what you are trying to do. To do a cruve fit suggests you have some sort of data. You haven't explained the format of the data or how your notation relates to it. For example, it isn't clear whether your data is triples of the form (x,y,z). If it is, then why would you expect to fit a curve to such data by picking a value for the single parameter b ?

 

[mattskie]

It doesn't appear that you are familiar with the way the LINEST function works, b ends up being the error +/- to fit the curve correctly. Much in the same way as bi-linear provides a b. I made the variables x,y,z for simplicities sake. If you need the data to provide the equation of a tri-quadratic equation (which you shouldn't, there should be an equation much like the bi-linear x+x^2+y+y^2+xy+b)

http://tinypic.com/view.php?pic=2uzxvdt&s=8 <---graph
http://tinypic.com/view.php?pic=2u3wsqt&s=8 <---data