Principal component and multiple regression analysis in modelling of grade and factors affecting the students' performance in Pre-Calculus

Abstract

Predicting students' academic performance is helpful for educational institutions striving to improve students' success and provide support to those at risk of getting a failing grade. This paper presents an empirical study that uses students' academic performance and demographic data to predict the Pre-Calculus grades of Senior High School students in the STEM track during the first quarter of the 2023-2024 academic year, employing both multiple linear regression and principal component regression methods. Multiple regression analysis was used to fit the Pre-Calculus grade using forty-three (43) school-related variables
as predictors. A variable selection method based on high loadings of varimax rotated principal components was used to obtain subsets of the predictor variables to be included in the regression model of the Pre-Calculus grade. Result shows that while MLR exhibits slightly higher R2, lower MSE, and lower MAE compared to MLR-PCA, the differences are negligible. Attending a private school, achieving high grades in core subjects such as Mathematics, Science, English, and Filipino and performing well on assessments such as pre-test, post-tests, and entrance exams play a significant role in the grade of the student in Pre- Calculus. Moreover, the variable regular attendance, fewer past class failures, and shorter commute times seems to contribute improvement of the student's grade in Pre-Calculus.