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I was looking at the information provided as part of the "A complete guide to 3D visualization device system in R - R software and data visualization” and was hoping that someone could provide a layman's explanation or interpretation of what the ellipsoid generated by ellipse3D() function represents.

Looking at the description on the Inside-R site, it describes it as

outline of a confidence region for three parameters.

What's not clear to me is what that confidence region represents (e.g., probability of new observation, location of true mean, etc.)? Thanks in advance!

Igor F.
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Dave
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1 Answers1

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The ellipsoid represents a tri-variate normal distribution, whose shape is determined by the covariance matrix. The semi-axes are the variances. You can think of it as a higher-dimensional generalization of the univariate normal distribution. If you have a point cloud in 3D, you can find the points that are inside the ellipsoid, with a certain probability.

SushilC
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    I believe this question wants the answers to focus on how these ellipsoids give *confidence intervals* and how that should be interpreted. – whuber Jul 19 '16 at 14:07