Letand

Show that the least-squares line for the data.(x₁; y₁).......(x_n,y_n) 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 

Transcribed Image Text:

1 x = = (x₁+ n + Xn)