The constant rise in the consumption of resources puts the environment under pressure. Most resources are non-renewable in nature, which is why they must be utilized with great care. For this reason, the European Union devotes increasingly more attention to their efficient use. It deals with these aspects, making an effort to maintain the long-term competitiveness and to secure sustainable development in line with all of the related environmental impacts. In this context, several goals have been set out, to which the individual EU member states are bound. A method for monitoring resource efficiency was developed, consisting of indicators, the aim of which is to assess the efficiency of the use of soil, water, energy, with the most fundamental one being resource productivity. The results of the efficiency of use of the individual resources in the member states greatly differ, even without further investigating the links and correlations between the indicators. Research on the interrelationships of the individual indicators in terms of mutual influence has not yet been completed. The aim of our study was to define the correlation between the main indicator, resource productivity, and the other indicators at the level of the EU and its member states. For this purpose, we prepared a database with data which, for the sake of uniformity, were obtained from the publicly available Eurostat database. Subsequently, the data were analyzed and evaluated using the statistical software JMP 15 by a regression and correlation analysis. By using the multiple regression analysis, we created a model describing the significance of the impact of the observed variables on the resulting resource productivity of the EU member states. Generally, there is a positive correlation between the resource productivity and the Eco-Innovation index, as well as the utilization rate of recycled materials. For the sake of comparison, we developed a regression model at the level of the V4 countries, with the aim of evaluating the impact of the historical background of the countries on their contemporary ability to reach the goals set out by the environmental policy. The V4 countries are lagging far behind in meeting all of the environmental policy objectives, not only in tracking the main indicator (resource productivity) on which the multiple regression analysis is based. It was interesting to find that the multiple regression model at the V4 level does not include the indicators defined by the EU level model, the key ones, in this case, being water productivity, energy dependence, energy productivity, and environmental tax. This finding may also, after further analyses, be the key for other countries joining the EU in the future, in defining the weaknesses of the newly acceding states in terms of the EU’s move towards a circular economy.