Evaluate Goodness of Fit - Ellipsoid

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Alessandraro
Alessandraro el 13 de Jun. de 2019
Editada: Andrew McLean el 14 de Jun. de 2019
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?
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Alessandraro
Alessandraro el 14 de Jun. de 2019
I am sorry, the question was if I can calculate the determination coefficient (R^2) and how.
Matt J
Matt J el 14 de Jun. de 2019
I don't think so. R^2 is only defined for fitting problems where you have independent and dependent variables.

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Andrew McLean
Andrew McLean el 14 de Jun. de 2019
Editada: Andrew McLean el 14 de Jun. de 2019
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.

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