Question: Fit N-dimensional data to an undetermined polynomial

MAPLE Users,

Suppose I have a set of points in some N-dimensional space.  I would like to obtain a simple polynomial that

best fits the data.  I do not know in advance the form of the function, but a simple function that does not overfit

the data would probably be OK.  By "simple" I mean the smallest degree with or without cross-terms that gives a

decent fit.  My data set will typically be an external comma or tab separated text file.

Also, if there is some means to visualize the points in the space and on a surface (if appropriate) that would be excellent.  I will also probably need some simple measure of fit of the function to the data.

I will then need to compute the Jacobian matrix, and eventually the metric tensor for this data set. I apologize in advance if this is a FAQ or a trivial question! 

Does anyone have any MAPLE worksheets that illustrate how to do this, or is there a tutorial somewhere?

Thank you.

Jim Metz

Abbvie