A Note on Estimation in Straight Line Regression When Both Variables are Subject to Error

Let yi = α + βxi + εis xi = ξi + δis i = 1, 2, ···, N, N ≥ 3, where (εis δi)s i = 1, 2, ···, N are independent bivariate normal with zero means, variances σ ε2 σδ2 and correlation ρ, the ξi being unknown constants at least two of which are distinct. Let τ = (N−1)−1 ΣN i=1 (ξi − ξ)2/Σ δ2 and let . A recent article by Richardson and Wu gives, among other things, the expected value and m.s. error of b, when ρ = 0. This note generalizes their results, using a different method, to the case of ρ ≠ 0.