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I have sets of data that ideally should be constrained to elliptical bounds. I am looking for a method to see how elliptical a set of data is. My inital approach involved mean-centering and normalizing my data, calculating the angle of the point relative to the origin, finding the frequency distribution of this data and comparing it to a standard distribution. Graphically this works well for clearly elliptical data, but as the data approaches a circular bound (which is also valid) the distribution becomes flat and the comparison poor.

Is there a good statistical way to determine how well a set of data is fit by a elliptical bound? What methods are available for n-dimensional ellipsoids?

Please let me know if you need any more details and thanks for the help.

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# Elliptical-ness of Data

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