Estimation linear non-elementary regression models using ordinary least squares

When constructing regression models, the problem of choosing a structural specification is paramount. To date, a great variety of such specifications have been developed. This paper provides a brief description of the following forms of relationship between variables: linear regression, linear elementary regression, linear multiplicative regression, Leontief production function, and index regression. Due to the mixing of linear and piecewise linear regressions, a new specification has been formulated - linear non-elementary regression, in which regressors are both input variables and binary operations of all possible combinations of their pairs. It is shown that the assignment of specific values to certain parameters of such models makes them quasilinear, which makes it possible to estimate them using the ordinary least squares. Areas of definition of these parameters are established. An algorithm for approximate estimation of linear non-elementary regressions using the ordinary least squares is developed. The operation of the algorithm is demonstrated by the example of modeling electricity consumption in the Irkutsk region. The quality of the constructed linear non-elementary regression by the coefficient of determination turned out to be higher than that of the previously obtained models. It is shown that in linear non-elementary regressions, the nature of the influence of input variables on the output changes over time.

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