The article explores the interrelations between research and development (R&D), innovation activity, and economic growth in the Russian regions. To analyze these interrelations, the econometric framework is applied. Based on data for 2005–2013, panel regression with fixed effects and the Arellano–Bond model are constructed. Hypotheses about the significant impact of knowledge and socioeconomic conditions on regional growth have been tested, while the expenditure on R&D and technological innovation are used to analyze knowledge spillovers; and spillovers of socioeconomic conditions are modeled with a socioeconomic filter. The results of calculations indicate possible competition for labor in the industry when this indicator is included in the socioeconomic filter. The calculations also confirm the significant impact of expenditure on technological innovation and spillovers on technological innovations for regional economic growth. At the same time, knowledge has been more efficiently disseminated to regions with high absorptive capacity, as well as between regions with similar growth rates. The authors conclude that knowledge spillovers can have a significant impact on gross regional product per capita (GRP) growth. The results can be used by regional governments when formulating innovation policy.