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This study investigates how student engagement influences academic and career persistence intentions. Data from 370 graduate students in South Korea were analyzed using random forest regression to assess the predictive power of engagement across different models of academic and career persistence. Findings show that engagement-related factors far outweigh personal characteristics in explaining persistence. Academic persistence was driven by lab participation, collaborative projects, advisor relationships, and psychological belonging, whereas career persistence was shaped by emotional engagement in research, advisor interactions, and peer learning. The integrated model achieved the highest predictive accuracy for both outcomes. These results underscore the relational and emotional aspects of engagement, suggesting that graduate education should cultivate collaborative, research-rich, and supportive environments to strengthen persistence and professional commitment.