Let and Show that the least-squares line for the data.(x 1 ; y 1 ).......(x n, y

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Letand

Show that the least-squares line for the data.(x1; y1).......(xn,yn) must pass through (x̅,y̅). That is, show that x̅ and y̅ satisfy the linear equation

Derive this equation from the vector equation .Denote the first column of X by 1. Use the fact that the residual vector ϵ is orthogonal to the column space of X and hence is orthogonal to 1.]

Given data for a least-squares problem,the following abbreviations are helpful:

The normal equations for a least-squares line x may be written in the form 

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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