Assessing Linear FAME-Property Relationships in Heterogeneous Biodiesel Databases: A Sequential Cross-Validated Subset-Selection Approach

Linear correlations based on fatty acid methyl ester (FAME) composition provide a transparent approach for estimating biodiesel properties, although their applicability to heterogeneous literature databases depends on the existence of a consistent composition-property structure. This work assesses linear relationships for density, kinematic viscosity, flash point, and lower and higher heating values using the normalized shares of palmitic, stearic, oleic, linoleic, and linolenic esters. A sequential nested leave-one-out procedure selects, at each stage, the observation whose exclusion maximizes the cross-validated performance of the remaining subset. The complete procedure is also applied to response-permuted, or Y-randomized, surrogate databases. The archived operating point is the first stage at which the fitted real trajectory reaches Rfit2 ≥ 0.60, while the real-versus-permuted differential Δ(k) compares the fitted linear compatibility of the actual FAME-property pairing with the mean fitted linear compatibility obtained after response randomization. Because sustained removal also raises the surrogate trajectories, the fitted R2 alone is not interpreted as evidence of a composition–property relation; the comparison relies on Δ(k). Exploratory data analysis first characterizes the original databases through target-property distributions, descriptive statistics, and literature-source and feedstock representation. This baseline is then extended by comparing the original and retained databases in terms of literature-source and dominant-FAME retention, target-property distributions, principal-component coverage, and Spearman rank-correlation structure, showing that the retained subsets largely preserve the main compositional characteristics of the original databases. Cook’s distance and Williams plots provide independent influence flags for a substantial, but incomplete, fraction of the selected observations, including response-inconsistent and high-leverage cases. Selected observations are interpreted as operationally incompatible with the five-FAME linear description at their respective selection stages; possible causes include influence, omitted descriptors, or nonlinear behavior. The combined statistical, representational, and physical evidence supports conditional linear correlations for kinematic viscosity, flash point, and higher heating value, in decreasing order of feasibility. In contrast, the selected density and lower-heating-value databases do not provide sufficient evidence for reliable linear correlations using the five-FAME representation. Semisynthetic manufactured databases show above-blind enrichment of planted response mismatches and generally reproducible coefficient recovery, with property-specific exceptions. The proposed framework therefore provides a systematic means of identifying and characterizing linear-compatible regimes within heterogeneous biodiesel property databases.