The quality of regression models must be evaluated by many indicators. Quality criteria can be the minimum of square sum or absolute values of deviations of the predicted values from the true ones, the adequacy of value and sign of the coefficients in the regression equations, the model robustness, the minimum of signs necessary to fulfil other indicators, and much more. When constructing regression equations using standard programmes, it is quite difficult to simultaneously take into account several of the listed indicators. The aim of the article is to demonstrate that building regression models based on mathematical programming problems allows simultaneously considering a large set of requirements for the solution quality within one model. The scientific novelty lies in the fact that this approach makes it possible to create more complex regression models that take into account the specifics of particular practical problems. For example, in the general sample, there may be different trends at the same time. In this case, it is necessary to find out how many regression equations are required to describe the available observations with a given accuracy. A special case of such a formulation is piecewise linear regression. Another example can be the need to predict multiple output parameters with a minimal set of identical input parameters. The article presents the practical results of applying the author’s approach to solving regression problems in agglomeration production and forecasting financial results for the banking sector