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I need help to understand and answer the following question.

I referred the following website to read about the confidence ellipsoids. https://www.visiondummy.com/2014/04/draw-error-ellipse-representing-covariance-matrix/

enter image description here

My answer would be:

a) Dataset 1 is more trustworthy. Because Dataset1 ellipsoid is smaller than Dataset2 ellipsoid.

b) The eigenvectors represent the direction of the largest spread of the data, whereas the eigenvalues define how large this spread really is.

i) I want to know if the ellipsoid is parallel to x-axis or y-axis , then whether that makes the experiment more trustworthy or it just depend on the axis length of the ellipsoids. ii)Is there a mathematical relation that relates the eigenvectors and eigenvalues to the confidence ellipsoids?

Thanks.

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  • $\begingroup$ On the face of it (b) makes no sense, because "the direction of the largest spread" evidently is unique whereas you are referring to the plural "eigenvectors." You might therefore want to reconsider that answer. $\endgroup$
    – whuber ♦
    Commented Apr 15, 2020 at 14:13
  • $\begingroup$ Ok, can I derive the confidence ellipsoid if I know the eigenvectors of the covariance matrix? If yes ,how? $\endgroup$
    – Gopal Krishna
    Commented Apr 15, 2020 at 14:43
  • $\begingroup$ Search our site. $\endgroup$
    – whuber ♦
    Commented Apr 15, 2020 at 15:27

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