Hence, a2 = (337.273/8) = 42.1591, which is approximately the value obtained previously in Chapter 3.

Properties of OLS Vector p

In the two- and three-variable cases we know that the OLS estimators are linear and unbiased, and in the class of all linear unbiased estimators they have minimum variance (the Gauss-Markov property). In short, the OLS estimators are best linear unbiased estimators (BLUE). This property extends to the entire p vector; that is, p is linear (each of its elements is a linear function of Y, the dependent variable). E(p) = p, that is, the expected value of each element of p is equal to the corresponding element of the true p, and in the class of all linear unbiased estimators of p, the OLS estimator p has minimum variance.

The proof is given in Appendix CA, Section CA.4. As stated in the introduction, the k-variable case is in most cases a straight extension of the two-and three-variable cases.


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