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There are two measurement error models in linear regression, the structural and the functional. Theoretical investigations and applications are concentrated on the structural model with jointly normally and identically distributed observations because there is no test for the slope in the functional model so far. This gap will be closed here for the model with one independent variable. Furthermore it is stated that the functional model is a natural extension of the classical linear regression model with one independent variable if there are errors of measurement in both variables. Moreover it is not postulated in the functional model that the expectations are equal. So the functional model is more realistic than the structural.

A test for the slope in the functional measurement error model