You'll find that it is a lot easier to do it in R: # lets first simulate a bivariate normal sample library(MASS) bivn <- mvrnorm(1000, mu = c(0, 0), Sigma = matrix(c(1, .5, .5, 1), 2)) # now we do a kernel density estimate bivn.kde <- kde2d(bivn[,1], bivn[,2], n = 50) # now plot your results contour(bivn.kde) image(bivn.kde) persp(bivn.kde, phi = 45, theta = 30) # fancy contour with image image(bivn.kde); contour(bivn.kde, add = T) # fancy perspective persp(bivn.kde, phi = 45, theta = 30, shade = .1, border = NA) ######################################################################### Hi, I've used the Mathematica to produce 3D graphics, contour plots of a bivariate normal distribution Now I want make these graphics in R, but i do not know how. I would like to: - Plot a 3D graph for some different variance matrix - Plot the contour plots - Find and try to plot (in the 3d graph ou contour plot) the (1-a)% confidence region based in a chi-square(a) with the degrees of freedom equal a 2 or bigger. Below is the Mathematica Notebook that i've used until now << "Graphics`PlotField`" NB[x_,y_]:=(1/((2 Pi)*Sqrt[a*b*(1-c^2)]))*Exp[(-1/(2*(1-c^2)))*( ((x-u)/Sqrt[a])^2 + ((y-v)/Sqrt[b])^2 - 2*c(((x-u)/Sqrt[a])((y-v)/Sqrt[b])) )] {{a,c}, {c,b}} = {{1,0}, {0,1}}; The covariance Matrix {u,v} = {0,0}; Mean vector Plot3D[NB[x,y],{x,-1.5,1.5},{y,-1.5,1.5}, AxesLabel->{x,y,z}, BoxRatios->{1,1,1}]; ContourPlot[NB[x,y],{x,-1,1},{y,-1,1}, Axes->True, AxesLabel->{x,y}]; 3d graph rotation Do[ Plot3D[NB[x,y],{x,-1.5,1.5},{y,-1.5,1.5}, PlotPoints->20, Mesh ->False, SphericalRegion ->True, Axes ->None, Boxed ->False, ViewPoint->{2 Cos[t], 2 Sin[t], 1.3}, BoxRatios->{1,1,1} ],{t, 0, 2Pi-2Pi/36, 2Pi/36}] Thanks, Rafael -- bertola at fastmail.fm -- love email again