Understanding, modeling, and predicting student performance in higher education poses significant challenges concerning the design of accurate and robust diagnostic models. While numerous studies attempted to develop intelligent classifiers for anticipating student achievement, they overlooked the importance of identifying the key factors that lead to the achieved performance. Such identification is essential to empower program leaders to recognize the strengths and weaknesses of their academic programs, and thereby take the necessary corrective interventions to ameliorate student achievements. To this end, our paper contributes, firstly, a hybrid regression model that optimizes the prediction accuracy of student academic performance, measured as future grades in different courses, and, secondly, an optimized multi-label classifier that predicts the qualitative values for the influence of various factors associated with the obtained student performance. The prediction of student performance is produced by combining three dynamically weighted techniques, namely collaborative filtering, fuzzy set rules, and Lasso linear regression. However, the multi-label prediction of the influential factors is generated using an optimized self-organizing map. We empirically investigate and demonstrate the effectiveness of our entire approach on seven publicly available and varying datasets. The experimental results show considerable improvements compared to single baseline models (e.g. linear regression, matrix factorization), demonstrating the practicality of the proposed approach in pinpointing multiple factors impacting student performance. As future works, this research emphasizes the need to predict the student attainment of learning outcomes.