Question: Let the regression equation between Y and Xs be given by i 0 1 1i 2 2i k ki i Y = ???? +????X +????

Let the regression equation between Y and X’s be given by i 0 1 1i 2 2i k ki i Y = ???? +????X +???? X +.......+???? X +???? , i i i ???? Y ???? x???????? ???? ???? , where i i E(???? |x ) = 0, and 2 2 i i i i Var(???? |x ) = ???? = ???? w , where i w is a non-stochastic variable which will be identical or function of X’s. Given a sample of observations on Y and X’s, discuss the technique to obtain the generalised least squares (GLS) estimator of ????. If the form of heteroscedasticity is 2 2 2 i i i 1i Var(???? |x ) = ???? = ???? X , then discuss the technique to obtain the GLS estimator of ???? .

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