density ellipse

Question

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

flo_kussener · Answer

Thank 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

jiancao · Answer

1. Density ellipse is computed based on an assumed bivariate normal distribution fit to x1 and x2:

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.