There is a Theorem on "Orthogonal Partitioned Regression" which says: "In the multiple linear least squares regression of y on two sets of variables X_1 and X_2, if the two sets of variables are orthogonal, then the separate coefficient vectors can be obtained by separate regressions of y on X_1 alone and y on X_2 alone. ..."

Stephany Wilkins 2022-10-25 Answered
There is a Theorem on "Orthogonal Partitioned Regression" which says:
"In the multiple linear least squares regression of y on two sets of variables X 1 and X 2 , if the two sets of variables are orthogonal, then the separate coefficient vectors can be obtained by separate regressions of y on X 1 alone and y on X 2 alone. ..."
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na1p1a2pafr
Answered 2022-10-26 Author has 16 answers
Two vectors v , w R n are orthogonal iff v t w = 0 where t indicates the transpose. Really, we're using the dot product given by v , w = v t w.
There is a different notion of orthogonality for matrices. Here's one definition of an orthogonal matrix: O M n ( R ) is orthogonal if O t O = I. Equivalently, this means that the columns of O are orthonormal, i.e., that they are orthogonal and have length 1.
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i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?
historical past/issues:
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