Evaluate Goodness of Fit - Ellipsoid

I have a set of 3D data points (x,y,z) and the quadratic form of an ellipsoid of equation

a*x^2 + b*y^2 + c*z^2 + d*xy + i*z - 1 = 0

with a,b,c,d,i known parameters.

How can I evaluate how well the equation fits the data?

[Matt J]

The norm of the left hand side?

[Alessandraro]

I am sorry, the question was if I can calculate the determination coefficient (R^2) and how.

[Matt J]

I don't think so. R^2 is only defined for fitting problems where you have independent and dependent variables.

Answer 1

[Andrew McLean]

One approach would be to calculate the distance of each point to the ellipsoid. Then your measure of goodness-of-fit could be the RMS distance of the points to the eliipsoid or the mean distance.