Processing math: 100%

 

 

 

Optimizing our parameters

We have defined the matrix X via the equations

y0=β0x00+β1x01+β2x02++βn1x0n1+ϵ0y1=β0x10+β1x11+β2x12++βn1x1n1+ϵ1y2=β0x20+β1x21+β2x22++βn1x2n1+ϵ1yi=β0xi0+β1xi1+β2xi2++βn1xin1+ϵ1yn1=β0xn1,0+β1xn1,2+β2xn1,2++βn1xn1,n1+ϵn1.

As we noted above, we stayed with a system with the design matrix XRn×n, that is we have p=n. For reasons to come later (algorithmic arguments) we will hereafter define our matrix as XRn×p, with the predictors refering to the column numbers and the entries n being the row elements.