In the article a new approach to regression models selection [diagnostics] is presented.
It covers the case of fixed sample and predefined set of potential factors/
exogenous variables. By using conventional criteria it is possible to select alternative
models with subsets of exogenous variables, for which the normality condition of
residuals is not rejected. The harmonicity condition, based on a generalization of
Hellwig’s coincidence concept, is then applied to these models. Nonexistence of simultaneously
rival, and harmonical regressions with normal residuals (RHN-regressions),
given the sample and the set of exogenous variables, signifies presence of data outliers
[atypical observations] in the sample. A class of regression trimming procedures
to test for outliers and adjust them so to apply the RHN-regression selection procedures
is proposed. Examples of application of the proposed procedures are based on
the data samples borrowed from classical sources on regression analysis.