Regularized Multivariate Linear Regression for Academic Performance Prediction: A Probabilistic Approach

Mingxuan Li

Abstract

The rapid digitalization of education has enabled the collection of high-dimensional student behavioral data. However, translating this data into actionable pedagogical interventions remains a challenge due to the ``black box'' nature of complex machine learning models. This study proposes a transparent, interpretable, and mathematically rigorous Ridge Regression framework (L2-Regularized Linear Regression) to predict student final exam scores. We ground our model in Maximum Likelihood Estimation (MLE) under the assumption of Gaussian noise. The optimization is performed using Batch Gradient Descent with adaptive learning rates. Acomprehensive ablation study is conducted on a dataset of 500 students to quantify the marginal contribution of behavioral features. The model achieves an

R^{2}

of

0.892

and an RMSE of

4.25

. Crucially, the regularization term (

λ = 0.1

) reduces the variance of the estimator, preventing overfitting on small sample sizes. Feature analysis reveals that Prior GPA explains

65%

of the variance, while Study Consistency serves as a critical multiplier. We demonstrate that for tabular educational data, regularized linear models provide a superior trade-off between predictive accuracy and interpretability compared to non-linear baselines like Support Vector Machines.

World Journal of Young and Excellent Scholars

Regularized Multivariate Linear Regression for Academic Performance Prediction: A Probabilistic Approach

Abstract

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