In the regression analysis, the most important stage in the construction of a model is specification. The aim of this work is to develop a new specification of the regression model. To do this, a new method is proposed for converting an arbitrary matrix into a vector - index transformation. An example of an index transformation of a matrix is considered. Particular cases of index conversion are shown. Using index transformation, a new specification of regression models has been developed, which is a generalization of the Leontief production function known in econometrics. To evaluate this model using the least squares method, its simplification is proposed. Using this simplification, a numerical example is considered. As a result, the approximation quality of the new regression specification turned out to be significantly higher than the quality of the classical multiple linear regression model.
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