The full least-squares method

This paper deals with the problem of the regression of measured quantities when measurement uncertainty affects both the regressed quantity and the independent variables. A new criterion is given, named the full least-squares method. A compact matrix notation is used for deriving the parameter vector of the regression model and its uncertainty variance-covariance matrix. Some examples of application of the novel method are given together with a comparison with the regression obtained by the generalized least-squares and the total least-squares methods.