Fig. 1.

The relative RMSEs of Model II to OLS for each estimated coefficient (β_r, β_f, β₁) are plotted as a function of the ratio of the true standard deviations, σ_x:σ_y (A), the number of random regressors, $x_r^{(s)}$ (B) and the accuracy of the ratio estimate (C). With increasing σ_x:σ_y ratios, model II regression has increased relative accuracy in β_r estimates compared to OLS with increasing σ_x:σ_y ratios. Comparison of the β_f, β_r, and β₁ error distributions formed is shown explicitly in the inlay for the point σ_x/σ_y =1 in (A). The gray column shows the OLS error and the white column shows the Model II error, the horizontal line is where the error is zero. In (C), for one unit σ_y, the estimated ratio μ_x was allowed to deviate from the ideal case, μ_x/σ_x = 1. The common point shared in (A, B, C) is located in (B) at ‘Number of Random Regressors’ = 1, and (C) at ‘Ratio of Estimate to Truth’ = 1.