The regional level is considered critical for the design and implementation of innovation policies. Regional actors also profit from spatial proximity and the knowledge transfer that results from effective formal and informal collaboration. Here, we examine regional determinants of innovation activity that are external to a firm. These determinants include: (1) regional innovation strategy, (2) foreign direct investment, (3) regional networking, (4) universities and educational institutions, (5) public financial support, and (6) regional economic performance. Using the data for Czech NUTS 3 regions, we perform a principal component analysis to detect three uncorrelated determinants, namely regional economic performance, regional networking, and regional innovation strategy. To demonstrate their effect on firm innovation activity, we also use the data from the Community Innovation Survey to investigate determinants of innovation performance that are internal to a firm. Specifically, we include firms' R&D investments and linkages. In this way, we evaluate the level of knowledge creation within firms as well as their capacity to access and absorb knowledge from outside. We use technological innovation activity as an output variable. Using logistic regression models, we examine interaction effects to demonstrate that (1) a regional innovation strategy is more effective in regions with strong regional networking and (2) firms participating in enterprise groups benefit from regional networking. These findings provide evidence for the interactive effects of regional determinants on firm innovation activity, implying that regional innovation policy should address the specific characteristics and needs of the firms in the region.