[Measurement errors and linear regression].

Abstract

The consequences of a measurement error of known variance in the explanatory variable of a linear regression were assessed. On the average, the ordinary least squares (OLS) method underestimated the regression slope, the bias increasing with the variance of the measurement error and the strength of the relationship. Simulation results showed that the corrected-for-the-error estimate slightly overestimated the slope, the bias increasing with the variance of the measurement error and the strength of the relationship, but rapidly decreasing when the number of observations increased. In all cases the corrected estimate has a larger variance than the OLS estimate, Nevertheless, the mean square deviation of the corrected estimate to the "true" slope value can be smaller than the OLS one, even for a relatively small number of observations (< or = 100). In those conditions, the corrected estimate might be preferred when a "good estimation" of the regression slope is needed. Whereas a measurement error in the dependent variable, does not bias the slope estimator, when it is independent of the error in the explanatory variable, this is not the case when both measurement errors are correlated. An example of the need to correct for such a correlation is given.