- 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
[Limit posts to Mathematica related solutions to this. Others send directly to the author -- Moderator] 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