This study investigates the integration of individual human traits into an empathetically adaptive educational robot tutor system designed to improve student engagement and learning outcomes with corresponding Engagement Vector measurement. While prior research in the field of Human-Robot Interaction (HRI) has examined the integration of the traits, such as emotional intelligence, memory-driven personalization, and non-verbal communication, by themselves, they have thus-far neglected to consider their synchronized integration into a cohesive, operational education framework. To address this gap, we customize a Multi-Modal Large Language Model (LLaMa 3.2 from Meta) deployed with modules for human-like traits (emotion, memory and gestures) into an AI-Agent framework. This constitutes to the robot's intelligent core mimicing the human emotional system, memory architecture and gesture control to allow the robot to behave more empathetically while recognizing and responding appropriately to the student's emotional state. It can also recall the student's past learning record and adapt its style of interaction accordingly. This allows the robot tutor to react to the student in a more sympathetic manner by delivering personalized verbal feedback synchronized with relevant gestures. Our study investigates the extent of this effect through the introduction of Engagement Vector Model which can be a surveyor's pole for judging the quality of HRI experience. Quantitative and qualitative results demonstrate that such an empathetic responsive approach significantly improves student engagement and learning outcomes compared with a baseline humanoid robot without these human-like traits. This indicates that robot tutors with empathetic capabilities can create a more supportive, interactive learning experience that ultimately leads to better outcomes for the student.