I was looking at a very nice answer here, where the question was applying a confidence region to some data.

If we plot some data as a scatter plot:

XData = RandomVariate[NormalDistribution[1,1], 100000];
YData = RandomVariate[NormalDistribution[1,1], 100000];

XYDATA = Transpose[{XData, YData}];

XYCoVarMat = Covariance[XYDATA];
XYMean = {Mean[XData], Mean[YData]};

            XYDATA, Frame->True, FrameLabel->{"X","Y"}, LabelStyle->16, AspectRatio->1,
            Epilog -> {
                            Opacity[0.32, Green], EdgeForm[{Green, AbsoluteThickness[1]}], Ellipsoid[XYMean, 4 XYCoVarMat],
                            Opacity[0.32, Blue], EdgeForm[{Blue, AbsoluteThickness[1]}], Ellipsoid[XYMean, 3 XYCoVarMat],
                            Opacity[0.32, Red], EdgeForm[{Red, AbsoluteThickness[1]}], Ellipsoid[XYMean, 2 XYCoVarMat],
                            Opacity[0.32, Yellow], EdgeForm[{Yellow, AbsoluteThickness[1]}], Ellipsoid[XYMean, 1 XYCoVarMat]

I was wondering if anyone knew a way of filtering the data using this approach for example only select data that is with the ellipsoid boundary of Ellipsoid[XYMean, 1 XYCoVarMat]?

  • 3
    $\begingroup$ Would With[{rmf = RegionMember[Ellipsoid[XYMean, 1 XYCoVarMat]]}, Select[XYDATA, rmf]] work for you? $\endgroup$ Nov 15, 2019 at 16:09
  • 5
    $\begingroup$ It would work wonderfully. I'm starting to wonder if you are actually written purely from Mathematica functions. Thanks! $\endgroup$
    – user27119
    Nov 15, 2019 at 16:14
  • $\begingroup$ @J.M.willbebacksoon I don't know if you want to post an answer yourself or not, but given you provided the solution I feel you should get credit. If credit doesn't concern you I will accept ThatGravityGuy's answer so that the question is completed and helps users who find this question. $\endgroup$
    – user27119
    Nov 16, 2019 at 13:15
  • 1
    $\begingroup$ Please accept ThatGravityGuy's answer if you think you found it useful. $\endgroup$ Nov 16, 2019 at 13:24

1 Answer 1


As @J.M. pointed out in the comments, the key here is the function RegionMember. Since you already know the region that you want to work with, namely Ellipsoid[XYMean, 1 XYCoVarMat], you can use Select as

With[{rmf = RegionMember[Ellipsoid[XYMean, 1 XYCoVarMat]]}, Select[XYDATA, rmf]]



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