Errors-in-variables model

Summary

An errors-in-variables model is a regression model in which the regressors are measured with error, not only the response. In that case ordinary least squares on the observed regressors is biased and not consistent. In the simple linear case the slope is pulled towards zero, an effect called attenuation or regression dilution. Consistent estimation needs extra information, such as the ratio of the error variances, repeated measurements, or instrumental variables. Deming regression and total least squares are methods for such models.