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A criterion is proposed for testing hypothesis about the nature of the errorvariance in the dependent variable in linear model, which separates correctlyand incorrectly specified models. In the former only measurement errorsdetermine the variance (i.e., dependent variable is correctly explained byindependent ones, up to measurement errors), while in the latter the modellacks some independent covariates (or has nonlinear structure). The proposedMEM-V (Measurement Error Model Validity) test checks the validity of the modelwhen both dependent and independent covariates are measured with errors. Thecriterion has asymptotic character, but numerical simulations outlinedapproximate boundaries where estimates make sense. A practical example of theimplementation of the test is discussed in detail; it shows ability of the testto detect wrong specification even in seemingly perfect models. This type ofrelation between measurement errors and model specification has not beenstudied before, and the proposed criterion may stimulate future research inthis important area.

Does Regression Approximate the Influence of the Covariates or Just Measurement Errors? A Model Validity Test