Two ?'s:Permuting a data matrix and projection operator

Thu, Sep 20, 2001 4:18 AM

I don't really understand what dou you want...
The expression of the projection operator on subspace engendered by a 
matrix X is:
PX=X%*%(t(X)%*%Dn%*%X)-%*%t(X)%*%Dn
where Dn is a diagonal matrix of row weight and (t(X)%*%Dn%*%X)- is 
generalized inverse of (t(X)%*%Dn%*%X).
In multivariate regression analysis you use:
y=PX%*%y+error=a+bX1+cX2+...+error
But if you want a regression without term a (i.e. orthogonal to 
vector (1,1,...1), you must centered matrix X.

Is it what you want ?

St?phane DRAY
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Biom?trie et Biologie ?volutive - Equipe "?cologie Statistique"
Universite Lyon 1 - Bat 711 - 69622 Villeurbanne CEDEX - France

Tel : 04 72 43 27 56			   Fax : 04 78 89 27 19
       04 72 43 27 57 	   E-mail : dray at biomserv.univ-lyon1.fr 
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Two ?'s:Permuting a data matrix and projection operator

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