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The features of the ordinary least squares method, which gives a possible wayto a solution of the overdetermined systems of algebraic equations and allowsto estimate the uncertainties of the obtained solutions, are considered. As theimportant physical example we define four-loop QCD coefficients in thedependence of the relation between pole and running heavy quarks masses on thenumber of light flavors, using the existing results of numerical supercomputerbased calculations of the corresponding four-loop contributions at differentfixed numbers of light flavors. Stability of the found solutions to the numberof the considered equations and unknowns is demonstrated and supported by thePearsons's $\chi$-squared test.

theoretical and mathematical physics

The least squares method: application to analysis of the flavor  dependence of the QCD relation between pole and $\rm{\overline{MS}}$-scheme  running heavy quark masses