The article presents first results of statistical hypothesis testing of institutional matrices theory. Using cross-country analysis, we discovered a significant correlation between climate characteristics and dominance of X/Y-matrix institutions of the nation-state. We used data mining techniques, including methods of principal component analysis and variants of optimal valid partitioning, as well as a set of pattern recognition methods. Sample of 65 countries was used. Our data base included 116 initial indicators obtained from open sources and 15 calculated integral indicators. Computation variants were based on different combinations of indicators and different methods of analysis. We have taken into account non-linear relationship between the indicators. Our hypothesis about a correlation between climate characteristics for the nation-state territory and the dominance of the X- or Y-matrix institutions was confirmed with a probability of 89 to almost 100%. Results are discussed and correlation is explained in conclusion.