Study of nonlinearity criteria for additive power regressions

Mikhail P. Bazilevskiy, Anna V. Karaulova

Irkutsk State Transport University

This article is devoted, first of all, to the study of the behavior of the «area» non-linearity criterion for additive power regressions with one explanatory variable depending on the degree. This criteria was examined for monotonicity and it is proved that its limits at infinity are equal to one. Based on the proved theorem, the concept of «funnel of nonlinearity» is introduced. It is shown how with the help of «nonlinearity funnels» it is possible to control the degree of nonlinearity for additive power regressions when estimating. A new criteria of non-linearity is proposed, calculated as the difference between unity and the value of the coefficient of determination in a linear regression of the dependence of the explanatory variable on the same variable raised to a power. It has been established that the proposed criterion is correct to use only on large samples.

additive power regression, criteria of non-linearity, coefficient of determination, “funnel of nonlinearity”