london-journal-of-research-in-science-natural-and-formal London Journal of Research In Science: Natural and Formal 2631-8490 2631-8504 JournalsPress 10.34257/LJRS226874UK 226874 Statistical Data Approximations by a New Method and Its Engineering Applications New Linear Approximation by Distance Minimization OshkhunovMuaed M. TlibekovAleksey Kh. DoskoSergey I. Russia, Kabardino - Balkarian State University Russia 26 9

A new method of approximation by linear functions of random points specified in the Cartesian coordinate system is proposed and tested. The coefficients of the equation are determined from the condition of the minimum sum of the squares of the distances to the given points. In contrast to the classical method of approximation by linear functions, the proposed method does not lead to the uniqueness of the solution. A brief summary of the theory of the new method and its application is given. In particular, the following problems are considered: approximation of a random numerical field; interpolation of experimental data; analysis of the variance of the results of experiments; optimal placement of machine-building equipment; forecast of the number of products. The results of the calculations showed the high efficiency of the proposed method for solving practical problems.

 least squares method linear regression distance minimization piecewise linear variance analysis optimal placement predictive analytics. Full Text

A new method of approximation by linear functions of random points specified in the Cartesian coordinate system is proposed and tested. The coefficients of the equation are determined from the condition of the minimum sum of the squares of the distances to the given points. In contrast to the classical method of approximation by linear functions, the proposed method does not lead to the uniqueness of the solution. A brief summary of the theory of the new method and its application is given.  In particular, the following problems are considered: approximation of a random numerical field;  interpolation of experimental data; analysis of the variance of the results of experiments; optimal placement of machine-building equipment; forecast of the number of products. The results of the calculations showed the high efficiency of the proposed method for solving practical problems.