       3D Statistics?

• To: mathgroup at smc.vnet.net
• Subject: [mg29290] 3D Statistics?
• From: Moranresearch at aol.com
• Date: Mon, 11 Jun 2001 04:38:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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I thought I'd ask this question to the group.
What approach would you recommend.
I have two data sets in 3-space (x,y,z) with about 200 cases. One is
attempted change (xt,yt,zt) and the other is actual change (xc,yc,zc). I want
to come up with a transfer function that relates attempted change to the
actual change. attempted = f (actual). The inverse of this transfer function
will be used to choose the attempted change to give a desired actual change.
Now the  variables x,y,z may influence one another . So I could the following
regressions:
xt = f( xc,yc,zc,xc^2,yc^2,zc^2,xyc,xzc,yzc)
yt = f( xc,yc,zc,xc^2,yc^2,zc^2,xyc,xzc,yzc)
zt = f( xc,yc,zc,xc^2,yc^2,zc^2,xyc,xzc,yzc)
Giving a total of 27 coefficients and 3 constants.
I could look at the p-values of the terms and eliminate the non-significant
ones and repeat the regression with the reduced set of terms, so I'm not just
fitting noise emperically.
In each regression I could eliminate the outliers (>2SD) to tighten up the
data and repeat the regression. The problem with this I want to eliminate the
entire triplet (x,y,z) from the analysis not just a part of it.

In reality I want the transfer function to minimize the Euclidian distant
between the corresponding data points( i ).
((xti-xc)^2+(yti-yci)^2+(zti-zci)^2)^1/2
Is there a standard way of handling these 3D regression problems? What do you
suggest?
Thank you. John

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