Date: Mar 9, 2011 7:03 AM
Author: Hagwood, Charles R.
Subject: how to resize the plot of two ellipses

If I plot the following ellipses on the same axes , then the left
ellipse is much too small. Is there a way to redo the plot with the left
ellipse looking larger?

dat1 = dat1={{0.4337088920,.217018691},
{0.406673987,0.21247881},{0.429538614,0.219284756},{0.435436816,0.219360297},{0.433708892,0.219415037},{0.434859313,0.220394942}};

dat2={{2.057100439,0.837794005},{2.148339169,0.868515281},{2.143940655,0.864046805},

{2.148432958,0.874271059},{2.183485822,0.880743617},{2.19696413,0.892192841}};

p1=ListPlot[{dat1,dat2}, Frame->True,Axes->False];

mx1=Mean[dat1[[All,1]]];

my1=Mean[dat1[[All,2]]];

c1={mx1,my1}

mx2=Mean[dat2[[All,1]]];

my2=Mean[dat2[[All,2]]];

c2={mx2,my2}

cov1=Covariance[dat1];

cov2=Covariance[dat2];

n=Length[dat1];

falpha=Quantile[FRatioDistribution[2,n-2], Sqrt[.975]];

r1=2*((n-1)/(n-2))*falpha/n;

r2=2*((n-1)/(n-2))*falpha/n;

f1[x_,y_]:={x-mx1,y-my1}.Inverse[cov1].{x-mx1,y-my1}

f2[x_,y_]:={x-mx2,y-my2}.Inverse[cov2].{x-mx2,y-my2}

p3=ContourPlot[f1[x,y]==r1,{x,.4,.6},{y,.2,.3},Frame->None,PlotRangePadding->{Scaled[3],Scaled[2]}];

p4=ContourPlot[f2[x,y]==r2,{x,2,2.4},{y,.8,.95},Frame->None];

data=Join[dat1,dat2]

model=LinearModelFit[data,x,x]/
/p2=Plot[model["BestFit"],{x,0,2.6}];

Show[{p1,p2,p3,p4}]