Modified Method Approximation of Empirical Dependency

The article presents a practical problem that arises in a number of applied areas in the approximation of experimental data using the least squares method. In a number of engineering applications there is a need to present these data in the form of empirical formulas of power, exponential and other types, to present the desired dependence in the form of a polynomial. In this case, use the alignment of the original variables. After the transition to the main variables, the proximity of the experimental points to the empirical polynomial does not determine this proximity in the final relation. The paper presents an amendment that ensures this proximity, provides specific types of empirical formulas for which the corresponding systems of corrected normal equations are obtained. The considered example of application of the refined technique leads to a more accurate approximation of empirical dependence.