Journal of Data Science

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.

Forecasting is essential for optimizing resource allocation, particularly during crises such as the unprecedented COVID-19 pandemic. This paper focuses on developing an algorithm for generating k-step-ahead interval forecasts for autoregressive time series. Unlike conventional methods that assume a fixed distribution, our approach utilizes kernel distribution estimation to accommodate the unknown distribution of prediction errors. This flexibility is crucial in real-world data, where deviations from normality are common, and neglecting these deviations can result in inaccurate predictions and unreliable confidence intervals. We evaluate the performance of our method through simulation studies on various autoregressive time series models. The results show that the proposed approach performs robustly, even with small sample sizes, as low as 50 observations. Moreover, our method outperforms traditional linear model-based prediction intervals and those derived from the empirical distribution function, particularly when the underlying data distribution is non-normal. This highlights the algorithm’s flexibility and accuracy for interval forecasting in non-Gaussian contexts. We also apply the method to log-transformed weekly COVID-19 case counts from lower-middle-income countries, covering the period from June 1, 2020, to March 13, 2022.