This work aims to explain the behavior of the multi-drug resistance (MDR) percentage of Pseudomonas aeruginosa in Europe, through multivariate statistical analysis and machine learning validation, using data from the European Antimicrobial Resistance Surveillance System, the World Health Organization, and the World Bank. We ran a multidimensional data panel regression analysis and used machine learning techniques to validate a pooling panel data case. The results of our analysis showed that the most important variables explaining the MDR phenomena across European countries are governance variables, such as corruption control and the rule of law. The models proposed in this study showed the complexity of the antibiotic drugs resistance problem. The efforts controlling MDR P. aeruginosa, as a well-known Healthcare-Associated Infection (HCAI), should be focused on solving national governance problems that impact resource distribution, in addition to individual guidelines, such as promoting the appropriate use of antibiotics.