Stability of correlation coefficient to “outliers” used in regression analysis

Abstract

The question of the stability of the correlation coefficient in the presence of “emissions”, which in the regression analysis is often a consequence of the law of distribution of error, is excellent from the normal, for example, lognormal or normal with “severe cases”, is considered. In this case, they can not be rejected or corrected and remain in the training sample. At the same time there is a bias of the regression model in the direction of deviations. In addition, due to the change in the correlation coefficients in the emission factors, a change in the structure of the model is possible. The purpose of the work is to determine how large the displacement of the correlation coefficient can be, depending on the size of the coefficient itself, the method of its calculation, the magnitude of the emission, and the size of the sample for the various correlation coefficients.