Evaluating the Accuracy of Minimum Admission Score Threshold Projections Using Linear Regression and Shrinkage-to-Mean on SNBT Data

Abstract

This study evaluates, out-of-sample, the accuracy of two methods for projecting minimum admission score thresholds for the SNBT selection track: per-series linear regression (program × degree-level combinations) and shrinkage-to-mean, using 2023–2025 historical data tested against actual 2026 values across 47 series. Pure linear regression achieves MAE 39.40, RMSE 52.34, and 71.5% pass/fail classification accuracy, but exhibits optimistic bias (recall for the "fail" class only 0.543) and a systematic failure pattern: all 13 series with monotonic three-year training trends (consistently rising or falling) missed 100% in the mean-reversion direction during the evaluation year. The shrinkage-to-mean method, which blends linear projections with historical averages weighted by in-sample R², improves every metric (MAE 31.91, RMSE 43.58, accuracy 74.5%, "fail" recall 0.585) without additional data, yet does not change the bias direction and shows limitations for series with very short historical records (degenerate R²). This study formulates and compares two training-data-only early risk-detection mechanisms, with an explicit trade-off between discriminative power and recalibration requirements. Main contributions: genuine out-of-sample evaluation, identification of a universally consistent mean-reversion pattern, and concrete recommendations for designing similar trend-based prediction features.