Given that ci is an arbitrary constant, ơ2Ɛc2i is a positive i.e it is greater than zero. Thus var (β*)> var (β^). This

[answerhappygod]

Given that ci is an arbitrary constant, ơ2Ɛc2i is a positive i.e it is greater than zero. Thus var (β*)> var (β^). This proves that β^ possesses minimum variance property. In the similar way we can prove that the least square estimate of the constant intercept (α^) possesses minimum variance α^. Prove that the least square estimators of linear regression model are best, linear and unbiased (BLU) estimators.
Hint: a new estimator α*, which we assume to be a linear and unbiased estimator of function of α. The least square estimator α^ is given by α^ = Ɛ(1/n- X*ki)Yi
note: Ɛ is a summation symbol and X* is mean of X