Identifying key determinants of students' mathematics achievement using lasso regression

Abstract

Cognitive, socioeconomic, and instructional factors influence students' mathematics achievement. However, modeling these determinants becomes challenging when the number of predictors is relatively large compared to the available sample size, potentially leading to unstable estimates in conventional regression models. This study aims to identify key determinants of students' mathematics achievement using the Least Absolute Shrinkage and Selection Operator (LASSO) regression approach and to construct a parsimonious predictive model. The study employed a quantitative design involving 50 second-grade students from SMA Negeri 1 Subah, Batang, Central Java, Indonesia. Predictor variables included intelligence quotient (IQ), tutoring participation, parental income, parental educational background, study duration, teacher characteristics, and gender. Categorical predictors were converted to dummy variables, and all predictors were standardized before analysis. The optimal regularization parameter was determined using -fold cross-validation, and model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and coefficient of determination . The LASSO results indicate that only three predictors retain non-zero coefficients: IQ (  = 3.134), tutoring participation (  = 6.675), and parental income (  = 1.299). The resulting model achieves RMSE = 9.55, MAE = 8.23, and  = 0.061, suggesting limited explanatory power but improved model parsimony and interpretability. Coefficient stability analysis further shows that IQ is a relatively robust predictor, while tutoring effects exhibit higher variability across cross-validation folds. These findings highlight the importance of cognitive ability and supplementary academic support in shaping mathematics achievement, while also indicating that many relevant behavioral and environmental determinants remain unobserved. Methodologically, the study demonstrates the usefulness of regularized regression in handling small-sample multivariable educational data and producing interpretable sparse models. Future research should incorporate richer behavioral variables and explore nonlinear machine learning approaches to improve predictive performance.