Multivariate Regression Analysis of Academic Achievement: Identifying Key Determinants of Student Performance Outcomes
Keywords:
Multivariate Regression, Academic Achievement, Student Performance, xAPI Learning Analytics, Hierarchical Regression, Behavioral Engagement, Parental Involvement, Student Absence, Educational Data Mining, Learning Management System, OLS Regression, Determinants of LearningAbstract
This study presents a comprehensive multivariate regression analysis of academic achievement determinants using the xAPI Learning Analytics Education dataset, comprising 480 students enrolled in the Kalboard 360 Learning Management System. The research employs a hierarchical ordinary least squares (OLS) regression framework across four progressive model variants — Behavioral, Behavioral + Parental, Behavioral + Parental + Demographic, and Full Model — to quantify the incremental explanatory power of each predictor category on student performance outcomes measured on an ordinal three-class scale (Low = 1, Medium = 2, High = 3).
The full multivariate regression model achieves R² = 0.6849 and Adjusted R² = 0.6660 (F = 70.43, p < 0.001), explaining 68.5% of variance in student academic performance — a strong fit for an educational social science dataset. Hierarchical regression reveals that behavioral engagement predictors alone account for 52.3% of variance (Model 1), with parental involvement adding a significant 4.8 percentage points (ΔR² = 0.048, Model 2), demographic variables contributing a further 1.4 points (Model 3), and student absence contributing the largest single increment of 9.1 points (ΔR² = 0.091, Model 4). Ten-fold cross-validation confirms generalizability with CV R² = 0.657 ± 0.107 and CV RMSE = 0.425 ± 0.059.
Standardized coefficient analysis identifies Student Absence (β* = −0.380) and Visited Resources (β* = +0.202) as the two most influential determinants, followed by Raised Hands (β* = +0.181), Parent Answering Survey (β* = +0.137), and Parent-Guardian Relation (β* = +0.114). All regression assumptions are satisfactorily met: residuals are normally distributed (Shapiro-Wilk W = 0.997, p = 0.808), homoscedastic (Breusch-Pagan p = 0.182), non-autocorrelated (Durbin-Watson = 2.105), and all VIF values are below 2.5 — confirming the absence of problematic multicollinearity. Chi-square tests confirm that both Student Absence (χ² = 225.20, p < 0.001) and Parental Survey Participation (χ² = 95.36, p < 0.001) are highly significant categorical determinants of academic class.
