Criteria for internal reliability of linear least squares models

Abstract

An approach to analysis of internal reliability of linear least squares models is presented. It is based on the relationship between a single observational disturbance, i.e. a gross error or a blunder, and the model response being a certain pattern of distortions in the least squares residuals. Rigorous formulae describing this relationship in terms of internal reliability characteristics are derived both for the models with uncorrelated and correlated observations. A specific case of decorrelated observations is also taken into consideration. Finally, the criteria for the evaluation of the model internal reliability are proposed for all the above cases. It is worth mentioning that the criteria are obtained without resorting to any particular method of statistical testing. The theory is illustrated with two numerical examples, using simple measuring schemes.