CO2 hydrogenation into C2+-hydrocarbons is an attractive way to mitigate the green-house effect and provides new opportunities to produce valuable chemicals from the longer available raw material. The present manuscript introduces and experimentally validates a mathematical approach for identifying fundamentals affecting catalyst performance to provide guidelines for tailored catalyst design or for reactor operation. Literature data were analyzed by regression trees, ANOVA, and comparison of mean values. The Pauling electronegativity of dopant for Fe2O3 can be used as a descriptor for CO2 conversion and CH4 selectivity. In addition, combining alkali and transition metals as promoters for Fe2O3 is a promising route to enhance C2+-hydrocarbons selectivity and the ratio of olefins to paraffins. So-developed Mn-K/Fe2O3 catalyst (K/Fe of 0.005 and Mn/K of 0.4) hydrogenated CO2 to C2-C4 olefins at 300 °C with the selectivity of 30.4 % at CO2 conversion of 42.3 %. The selectivity to C2+-hydrocarbons (C2-C4 olefins are included) was 83.1 %.