Determination of emissions in the correlation and one-dimensional regression analysis

Abstract

In this paper, it is considered the method of determination of emissions in case of preliminary processing of data for correlation and one-dimensional regression analysis. The classification of emissions according to their nature is proposed. The algorithm developed on their determination is based on the consistent application of the jack-knife technique and the elements of distance calculations using the LSD-criterion, using instead of the mean values of the correlation coefficients and confidence intervals instead of the critical distances. The application of the algorithm is shown in the examples for different conditions of its use. The whole spectrum of possible conditions of application is considered: from those in which the method determines the emissions accurately, to those in which it does not work or the results of its work are ambiguous. It is established that described in the paper method allows to automatically determine the emissions, regardless of their nature, in the linear relationship between the variables. In the nonlinear relationship between variable emissions, they are determined in the case of linearization of variables (linearization in such situations is a prerequisite for data analysis). In questionable and uncertain cases, and with complex dependence, the algorithm defines outliers as those experiments, the removal of which leads to an improvement of the linear regression model (a priori, prior to its construction). The method does not work in the case of outliers that compensate each other, but in such situations, the presence of outliers does not lead to a significant shift of the model coefficients. The regression models have been constructed, which show changes in the characteristics and values of regression coefficients of the model under the influence of outliers. Using the method allows to identify questionable experiment points for further decision making. The method can be used in automated information processing systems, since it automatically guarantees the presence of outliers or improves the linear regression model.