(* Hadi's Method in Outliers *)



{m, s, cv} = IdentifyOutliers[.05, braindata];



<<Graphics`

QuadraticForm[x1_, x2_, m_, s_] :=

    ({x1 - m[[1]], x2 - m[[2]]}).Inverse[s].({x1 - m[[1]], x2 - m[[2]]});

plot1 = ContourPlot[QuadraticForm[x1, x2, m, s],

      {x1, m[[1]] - 3Sqrt[s[[1]][[1]]], m[[1]] + 3Sqrt[s[[1]][[1]]]},

      {x2, m[[2]] - 3Sqrt[s[[2]][[2]]], m[[2]] + 3Sqrt[s[[2]][[2]]]},

      DisplayFunction -> Identity, PlotPoints -> 100];

plot2 = ListPlot[braindata, Frame -> True, Axes -> False,

      DisplayFunction -> Identity, PlotStyle -> GrayLevel[1]];

plot3 = ImplicitPlot[QuadraticForm[x1, x2, m, s] == cv^2,

      {x1, m[[1]] - 4Sqrt[s[[1]][[1]]], m[[1]] + 4Sqrt[s[[1]][[1]]]},

      {x2, m[[2]] - 4Sqrt[s[[2]][[2]]], m[[2]] + 4Sqrt[s[[2]][[2]]]},

      PlotStyle -> GrayLevel[0.75], DisplayFunction -> Identity, 

      PlotPoints -> 100];

Show[{plot1, plot2, plot3}, DisplayFunction -> $DisplayFunction]