Weighted Least Squares suppose that we are fitting the line Y = Bo + B1x + , but the variance of Y depends on the level of x; that is, where the wi are constants, often called weights. Show that for an objective function in whole each squared residual is multiplied by the reciprocal of the variance of the corresponding observation, the resulting weighted least squares normal equations are

Find the solution to these normal equations. The solutions are weighted least squares estimators of B0 and B1

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i = 1, 2, .., n VY x) - σί - Σνυί β. Σν + βι ΣwA i=1 i=1 γ+ βι Σ ν-Σwμνη W;X;Vi