Construction of complicated multifactor models of optimal form on the basis of statistical data, when the physical essence of phenomenon is known

Abstract

The work contains computer-aided method of construction of multifactor and complicated models on the basis of experimental data. The models are non-linear but traditional (constructed with the help of the method with the preliminary transformation of the matrix of the initial data and the subsequent reverse transformation of the results). The models can have different form linear, multiplicative, exponent and so on. After the construction the models are improved using method of Givis and Hook, which improves their statistical characteristics and the quality of representation of the results of experiment. This work is in a certain way methodological. We have shown in it that having enough experimental data we can improve the quality of the models and formulas even those which already exist in school textbooks. On the other hand it is shown here that when knowing the essence of the phenomenon it is possible to choose an optimal model from the multitude of regressional models.