Abstract
Watson (1955) gave an inequality for the minimum efficiency of least squares as measured by the ratio of the generalized variances of the efficient and the inefficient estimators of the vector of regression coefficients. The inequality had been conjectured by J. Durbin. The proof given by Watson was faulty and was acknowledged as such by Watson (1967). This paper gives a proof for the inequality, which up to the present has remained a conjecture. The paper owes much to conversations over several months with J. Durbin and K. G. Binmore. Bloomfield & Watson (1975) have independently obtained a proof of the same inequality. The inequality asserts that
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