Problem 6. Consider the modelYi = Bogo(xi) + Broa (zi XXXXXXXXXXBrdr(zi) + eiwhere each ¢;(z;) for j...

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Problem 6. Consider the modelYi = Bogo(xi) + Broa (zi XXXXXXXXXXBrdr(zi) + eiwhere each ¢;(z;) for j = 0,1,2,..., k is a different nonlinear function of z= specified such thati @j(@i)di(wi) = 0 for all j,1;5 # I. Assume that ¢o(x;) = c for all i and for some ¢ # 0.(a) Show that the j™* element of the LSE of 3 is equivalent to the LSE of the coefficient parameteestimate from a model that includes only ¢;(x;).(b) Find an expression for the LSE of §.(c) Show that the difference in SSE between: (1) the model above with all k + 1 functions of z;and (2) a model analogous to that above but with only the first k functions of z; isEDD)where Br is the LSE of f.

Banasree · Accepted Answer

Ans.
6.a.
Yi = ꟗ0Ø0(xi) + ꟗ1Ø1(xi)+…………………+ꟗkØk(xi)+ei
PDF N(0,σ2I)
Y = 
Therefore
Y = ꟗØ + e………a
b.
to determine LSE of ꟗ0
we can rearrange a)
ꟗ = (y – e )/Ø
Or 
S(Øcap) = y^Ty – y^TꟗØ + Øcap ^T ꟗ^TꟗØcap
ᵟS/ᵟØ = 2ꟗ^TY +2ꟗ^Tꟗ CAP^T = 0
= >  Øcap = (ꟗ^Tꟗ0)^-1 ꟗ^TY
c.

Problem 6. Consider the model Yi = Bogo(xi) + Broa (zi XXXXXXXXXXBrdr(zi) + ei where each ¢;(z;) for j = 0,1,2,..., k is a different nonlinear function of z= specified such that >i @j(@i)di(wi) = 0...

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