Generalization of Non-elementary Linear Regressions

Earlier, the author developed a non-elementary linear regression consisting of a linear part and all possible combinations of min and max binary operations. This article is devoted to its generalization. For the first time a non-elementary linear regression with a linear part and all possible combinations of binary, ternary, ..., l-ary operations min and max has been introduced. The proposed model generalizes both linear regression and the Leontief function, and can be effectively used both for predicting and for interpreting the study object functioning. An estimation algorithm was developed using the method of least squares for non-elementary linear regressions without a linear part and with an l-ary operation min (max), i.e. regressions with specification in the form of a Leontief function. The essence of the algorithm is to form a set of possible values of slope coefficients, from which a point is selected with the minimum value of the residual sum of squares. A system of linear inequalities is identified that makes it possible to form such a set. Using the algorithm, a model of the gross regional product of the Irkutsk region was construct and its interpretation was given.