NONLINEAR CRITERIA OF QUASILINEAR REGRESSION MODELS
M. P. Bazilevskiy
Often, when choosing the best regression model in some given sense, this is can be non-linear regression. For example, with the implementation of the «competition» of models, the best regression may be quasilinear. The advantage of quasilinear regressions is the possibility of estimating them using the ordinary least squares. But the estimates obtained for the parameters of the quasilinear model rarely provide any meaningful interpretation. As a result, the constructed regression, provided that it has a high quality of approximation, can be used only for obtaining forecasts, which significantly reduces its practical significance. This paper is devoted to the problem of estimating the degree of nonlinearity of quasilinear regression models. Based on the Gini coefficient, a nonlinearity criterion for area has been developed. Also presented is its analogue – a nonlinearity criterion in length. These nonlinearity criteria allow us to estimate the degree of nonlinearity of both single-factor and multifactor quasilinear regressions. It is shown how the parameters of quasilinear regression can be interpreted with a low degree of nonlinearity. A specific numerical example of estimating the degree of nonlinearity of single-factor quasilinear regressions is considered. The developed criteria can be used in organizing the technology of «competition» of models to control the degree of their nonlinearity.
Keywords: : quasilinear regression, «competition» of models, interpretation of regression, Lorenz curve, Gini coefficient, nonlinear criterion.