# Cannot produce confidence contours of constant chi square for given data

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 I am trying to plot the experimental confidence regions that is 1 sigma, 2 sigma etc for a data which consists of experimental values of two quantities and corresponding delta chi square. So for the below mentioned sample dataI have tried this x = Function[a, ArcSin[Sqrt[a]]*(180/\[Pi])]@ Import["C:\\Desktop\\data1.txt", {"Data", \ {All}, {1}}]; y = Import[ "C:\\Desktop\\data1.txt", {"Data", {All}, \ {2}}]; data = {x, y}\[Transpose]; deltaChisq = Import["C:\\Desktop\\data1.txt", {"Data", \ {All}, {3}}]; (*define error Ellipse*) ErrorEllipse[data_, percLevel_, points_: 100] := Module[{eVa, eVec, coors, dchi, thetaGrid, ellipse, rEllipse}, {eVa, eVec} = Eigensystem@Covariance[data]; (*Get the coordinates of the data mean*)coors = Mean[data]; (*Get the perc[%] confidence interval error ellipse*) dchi = \[Sqrt]Quantile[deltaChisq, percLevel/100]; (*define error ellipse in x and y coordinates*) thetaGrid = Table[i, {i, 0, 2 \[Pi], 2 \[Pi]/99}]; ellipse = {dchi \[Sqrt]eVa[] Cos[thetaGrid], dchi \[Sqrt]eVa[] Sin[thetaGrid]}; (*rotate the ellipse and center ellipse at coors*) rEllipse = coors + # & /@ (ellipse\[Transpose].eVec)]; (*visualize results*) percentOneSigma = 66.3; percentTwoSigma = 95.4; Show[ListPlot[data], ListLinePlot[ErrorEllipse[data, percentOneSigma], PlotStyle -> {Thick, Red}], ListLinePlot[ErrorEllipse[data, percentTwoSigma], PlotStyle -> {Thick, Blue}], ListPlot[{Mean[data]}, PlotStyle -> {Thick, Red}], ListLinePlot[ErrorEllipse[data, 99.7], PlotStyle -> {Dotted, Black}], PlotRange -> All] Which giving me some ellipses, but I think they are not the exact confidence ellipses. Since this is a non linear data it should be a isocontour having constant chi square values. The contour should be the 2D 2 variable contour like this ![] Attachments: Answer