Abstract
<title>Abstract</title> <p>Regression-based analysis-of-variance (ANOVA) underpins much of quantitative biomedical inference, yet its classical formulation presumes predictor and response variables are observed without imprecision – an assumption routinely violated by instrument calibration bounds, biological variability, and sensor-reporting error. Interval, fuzzy, and Bayesian extensions each relax this assumption partially, but none provides a complete interval-valued analogue of the classical sums-of-squares decomposition together with a formally bounded F-statistic. This paper introduces Hybrid Neutrosophic Regression ANOVA (HNRA), which represents each observation as a neutrosophic interval and propagates this representation through ordinary-least-squares-based regression ANOVA using closed interval arithmetic. Four theoretical results are established: a decomposition theorem showing SST N ≈ SSR N + SSE N holds componentwise under interval arithmetic; a convergence theorem proving that HNRA reduces exactly to classical regression ANOVA as uncertainty vanishes; a monotonicity theorem establishing that all HNRA interval widths grow mono-tonically with measurement uncertainty; and a boundedness theorem proving strict positivity and finiteness of the interval-valued F-statistic, with a corollary guaranteeing uniform statistical significance whenever the interval lower bound exceeds the classical critical value. The framework is validated on a biomedical dataset of n = 60 adults relating muscle mass to age under ±10% response uncertainty and ±0.5-year predictor uncertainty, yielding F N = [116.52, 260.02], an interval lying entirely above the classical critical value F * 0.05,1,58 ≈ 4.00. A sensitivity analysis across five uncertainty levels (5%–25%) and a simulation study over 500 replications confirm that HNRA conclusions remain stable under increasing measurement imprecision, consistent with the proven theoretical properties. The framework requires no prior distributional assumptions, adds negligible computational overhead over classical OLS, and is directly applicable to clinical laboratory science, wearable-device analytics, and epidemiological inference under documented measurement uncertainty.</p>