The determinants of the presence of “Foreign Doctorate Students” among 36 European Countries for the period 2010-2019 are analyzed in this article. Panel Data with Fixed Effects, Random Effects, WLS, Pooled OLS, and Dynamic Panel are used to investigate the data. We found that the presence of Foreign Doctorate Students is positively associated to “Attractive Research Systems”, “Finance and Support”, “Rule of Law”, “Sales Impacts”, “New Doctorate Graduates”, “Basic School Entrepreneurial Education and Training”, “Tertiary Education” and negatively associated to “Innovative Sales Share”, “Innovation Friendly Environment”, “Linkages”, “Trademark Applications”, “Government Procurement of Advanced Technology Products”, “R&D Expenditure Public Sectors”. A cluster analysis was then carried out through the application of the unsupervised k-Means algorithm optimized using the Silhouette coefficient with the identification of 5 clusters. Finally, eight different machine learning algorithms were used to predict the value of the "Foreign Doctorate Students" variable. The results show that the best predictor algorithm is the "Tree Ensemble Regression" with a predicted value growing at a rate of 114.03%.