On the Assessment of Homogeneity in a Uniform Regression Model
УДК 519.65
Abstract
When conducting an exploratory analysis of the data and the subsequent construction of functional dependencies between the observed phenomena, it is often necessary to assess the degree of dependence between the studied data. The basis for obtaining such criteria with a probabilistic approach usually includes the correlation component of the sample. The choice of the used indicator directly depends on the methods of studying the sample, as well as the tools for constructing the model. In most cases, at the initial stage of modeling, it is precisely the homogeneity estimates of the sample that are studied, a good selection of which can reduce the complexity of constructing the relationship between the data.In this paper, we study a method for assessing the uniformity of sample data when constructing a uniform regression model. The first part of the paper describes the correlation coefficient for the L∞ regression, studies the interval of its change, describes the geometric interpretation and the algorithm for constructing this indicator. In the second part of the paper, we study the method of constructing an indicator of "concentration" of the sample. For this, formulas are derived that relate the correlation coefficient to the magnitude of the original sample. In conclusion, a description is given of the algorithms for constructing the considered indicators, and conclusions are drawn about the complexity of these algorithms.
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