07AlternativeParameterizations

# For example x 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0

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Unformatted text preview: l equations. For example, X= 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 Copyright c 2010 Dept. of Statistics (Iowa State University) µ τ1 β= τ2 τ3 y= y11 y12 y21 y22 y31 y33 Statistics 511 7 / 14 Normal Equations X Xb = X y ? n· n1 n2 n3 n1 n1 0 0 ? n2 0 n2 0 ? ? n3 0 0 n3 Set ﬁrst to zero ¯1· y 0 ¯2· − ¯1· y y ¯3· − ¯1· y y Set last to zero ¯3· y ¯1· − ¯3· y y ¯2· − ¯3· y y 0 Copyright c 2010 Dept. of Statistics (Iowa State University) y·· y1· = y2· y3· Sum to zero (¯1· + ¯2· + ¯3· )/3 y y y ¯1· − (¯1· + ¯2· + ¯3· )/3 y y y y ¯2· − (¯1· + ¯2· + ¯3· )/3 y y y y ¯3· − (¯1· + ¯2· + ¯3· )/3 y y y y Statistics 511 8 / 14 As noted before, such constraints are not necessary; we do not need to consider constraints when we work with generalized inverses. In 611, we study the issue of constraints much more carefully. We show that constraints of the form Mb = 0 produce a unique solution to the normal equations without restricting that solution to a proper subset of C (X) if...
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## This document was uploaded on 03/27/2014.

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