Explanatory and Predictive Model for Analyzing University Entrance Scores Using Linear Regression

Abstract

This research aims to analyze university entrance scores using linear regression models from both explanatory and predictive perspectives. A quantitative cross-sectional design was used with 545 university students, considering socioeconomic, academic, motivational, and demographic variables. An exploratory data analysis was conducted, revealing weak but statistically significant associations between entrance scores and variables such as income and years of study. Subsequently, an explanatory model was created using classical linear regression (OLS), incorporating a process for selecting the most significant variables. The final model yielded an adjusted R2 of 0.126, indicating limited explanatory power. The variables that showed statistically significant effects were years of study, type of high school attended, and the mother's educational level. Next, a predictive approach based on linear regression was implemented under the machine learning paradigm, using validation with training and test data, as well as automatic variable selection via LASSO regression. The performance metrics showed low predictive capacity, reflecting limitations in the model's generalizability. The final results of the study show that linear regression is useful for explaining significant associations but has predictive limitations; therefore, both approaches complement each other to offer a comprehensive perspective on university admissions.