Prediction Intervals and Group Variable Importance for Classification Models in University Enrollment Yield
Pub. online: 15 July 2026
Type: Statistical Data Science
Open Access
Open Access
Received
2 June 2026
2 June 2026
Accepted
1 July 2026
1 July 2026
Published
15 July 2026
15 July 2026
Abstract
Accurate forecasting of student yield is critical for academic institutions because enrollment projections directly affect resource allocation, course offerings, housing capacity, and budget decisions. Existing enrollment models primarily focus on predicting individual matriculation probabilities, whereas institutional planning depends on accurate prediction of the aggregate enrollment count together with its uncertainty quantification. Here we develop statistical methods for aggregate enrollment prediction and interval estimation under logistic, regularized regression, tree-based, and ensemble classification models. For unpenalized logistic regression, we derive an asymptotic prediction interval and a parametric-simulation interval that propagates coefficient uncertainty. For regularized and tree-based learners, we develop a model-agnostic bootstrap interval that captures selection, estimation, and predictive uncertainty in a unified framework. To interpret predictive structure, we introduce partial and marginal AUC measures to quantify the unique and standalone contributions of feature groups. Simulation studies show that the proposed intervals attain close-to-nominal coverage under well-calibrated and bootstrap-stable learners. Applied to University of Connecticut in-state freshman cohorts from 2020–2025, the proposed intervals contain the observed 2025 enrollment count while identifying the feature groups that contribute most strongly to the enrollment prediction.
Supplementary material
Supplementary MaterialThe online supplementary material consists of two files. The file supplement.pdf contains introduction of MoE (Section S.1), the theoretical derivations referenced in the main text (Section S.2), additional simulation results including the MoE DGP robustness study (Table S.1 and Figure S.1 in Section S.3), and expanded variable-importance figures (Figure S.2 in Section S.4). The file code.zip contains the complete R reproduction pipeline, including data generation, model fitting for all seven candidate methods, construction of the asymptotic, parametric-simulation, and bootstrap prediction intervals, and computation of the mAUC and pAUC feature-group importance measures. The archive also includes a synthetic dataset that preserves the structure of the applicant records used in the empirical analysis while protecting individual-level information.
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