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 harmonicitycondition, 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.