A2 Linearity And Unbiasedness Properties Of Leastsquares Estimators

CHAPTER THREE: TWO-VARIABLE REGRESSION MODEL 101

which shows that pS2 is a linear estimator because it is a linear function of Y; actually it is a weighted average of Yi with ki serving as the weights. It can similarly be shown that p91 too is a linear estimator.

Incidentally, note these properties of the weights ki:

1. Since the Xi are assumed to be nonstochastic, the ki are nonstochas-tic too.

4. £ kixi = £ kiXi = 1. These properties can be directly verified from the definition of ki.

For example,

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