The article is devoted to solving the actual problem of the construction of the linear multiple regression model, establishing the relationship between the economic indicators of the Russian Federation and the logistics infrastructure of the Federal districts. The obtained equation allows to identify the objects of the logistic infrastructure that have the greatest impact on the dependent variables, and to assess the degree of contribution of each component to the change in the resulting variable using multiple regression. The solution to this problem can be used in the elaboration of integrated development plans for the Federal districts of the country. The methodological tools of this study includes correlation analysis, Kolmogorov – Smirnov test, multiple regression analysis. The values of the indicators are taken for the period 2004-2016. As a result of the study using the IBM SPSS Statistics 20 program, the objects of the logistics infrastructure of the Federal districts that have the greatest impact on the economic performance of the Russian Federation were identified. It is shown that the transport and logistics infrastructures of St. Petersburg, the Krasnodar Territory, the Kirov, Sverdlovsk and Novosibirsk Regions as well as the volume of imports of goods in the Stavropol Territory and the number of transport enterprises in the Republic of Dagestan have the greatest impact on the dependent variables. An increase of the dependent variables by one percentage point will lead to an increase in the economic indicators of the Russian Federation from 0,74% to 1,01%.