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 that>i @j(@i)di(wi) = 0...

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Problem 6. Consider the model Yi = Bogo(xi) + Broa (zi) +... + Brdr(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 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 parameter estimate 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; is EDD) where Br is the LSE of f.