density ellipse<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />Hello,
Is there any document with more details about the calculation of density ellipse in Fit Y by X platform?
It is link to confidence interval (95%) but how is it computed?
And what if the variables don't have a normal distribution?
How would you compare this ellipse and Mahalanobis distance?
Thank for all information anyone can provide me about this density ellipse.
Florence
Re: density ellipseThank a lot Jian!
De : JMP User Community Administrator >
Répondre à : "jive-1409537905-hwqt-2-4nkh@community.jmp.com" >
Date : jeudi 2 juillet 2015 19:25
À : Florence Kussener >
Objet : Re: - density ellipse
JMP User Community<>
density ellipse
reply from jiancao<> in JMP SE Community - View the full discussion<>
Re: density ellipse1. Density ellipse is computed based on an assumed bivariate normal distribution fit to x1 and x2:
![P(x_1,x_2)=1/(2pisigma_1sigma_2sqrt(1-rho^2))exp[-z/(2(1-rho^2))],](http://mathworld.wolfram.com/images/equations/BivariateNormalDistribution/NumberedEquation1.gif)
For more details, check out http://mathworld.wolfram.com/BivariateNormalDistribution.html
The ellipsoid is drawn based on the fitted bivariate normal that covers a certain % of the data that you choose from the Density Ellipse menu (see JMP documentation Density Ellipse.)
2. If (x1, x2) don't follow a bivariate normal distribution, then usual arguments apply :-).
3. Mahalanobis distance measures the distance a data point is away from its multivariate mean taking into account the multivariate correlation structure of the data, while a density ellipsoid shows how strong the correlation of a pair of variables is using a fitted bivariate normal distribution.
To see their relations, you can use Multivaiate platform and run both Scatterplot Matrix and Outlier Analysis as seen below. They correspond fairly nicely.
