## 3 Results and Discussion
### Evaluation of the HS-BA\(\mu\)E/GC-MS Methodology
#### 3.2.2 Validation Parameters  
After optimizing the crucial experimental parameters--microextraction stage employing CN1 phase (3 h) at 35 \({}^{\circ}\)C and back-extraction stage utilizing _n_-C6 (100 \(\mu\)L) for 60 min--we proceeded with validation assays. These encompassed the assessment of analytical thresholds, linear dynamic ranges, as well as both intra- and inter-day precisions. Table 1 summarizes the validation data obtained from the proposed methodology (HS-BA\(\mu\)E/GC-MS) under optimized experimental conditions.  
Analytical thresholds were determined via LOD and LOQ, falling within the range of 5.0 to 49.5 \(\mu\)g/L. Generally, the LODs and LOQs align with values previously reported in other studies [7; 20; 21], except for those of thymol and cryophyllene oxide, where the values slightly exceeded expectations (0.1 \(\mu\)g/L \(\leq\) LOD \(\leq\) 0.5 \(\mu\)g/L).  
The linear dynamic ranges were established by analyzing multi-standard solutions of the six BVOCs, spanning from 20.0 to 100.0 \(\mu\)g/L for \(\alpha\)- and \(\beta\)-pinene, from 20.0 to 120.0 \(\mu\)g/L for limonene and 1,8-cineole, and from 50.0 to 100.0 \(\mu\)g/L for thymol and cryophyllene oxide. Calibration plots exhibited high determination coefficients (\(r^{2}\geq 0.9816\)), indicating strong linearity. However, assessing linearity based solely on the \(r^{2}\) parameter is insufficient, as it does not address data heteroscedasticity. Therefore, homoscedasticity was evaluated through lack-of-fit testing and residue dispersion [22]. The lack-of-fit test indicated a good fit for all calibration plots, suggesting homoscedastic data. Furthermore, residue plots displayed an unsystematic distribution of residues, confirming  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**BVOCs**} & **LOD (ug/L)** & **LOQ (ug/L)** & **Linear Range (\(\mu\)g/L)** & \multirow{2}{*}{**a**} & \multirow{2}{*}{**b**} & \multirow{2}{*}{**\(r^{2}\)**} & **Intra-Day Precision (\(n\) = 5; RSD,\%)** & **Inter-Day Precision (\(n\) = 3; RSD,\%)** \\ \hline \(\alpha\)-Pinene & & & & 0.0090 & 0.0614 & 0.9951 & 6.3–22.8 & 10.4–28.7 \\ \hline \(\beta\)-Pinene & & & & 0.0123 & \(-\)0.0563 & 0.9912 & 8.2–22.1 & 12.9–26.9 \\ \hline Limonene & & & & 0.0199 & 0.0846 & 0.9879 & 13.8–18.5 & 13.4–26.7 \\ \hline \multirow{2}{*}{1,8-Cineole} & & & & 0.0250 & 0.0557 & 0.9895 & 4.0–11.3 & 13.4–15.8 \\ \hline Thymol & & & & 0.0102 & 0.0195 & 0.9872 & 17.5–28.4 & 18.0–26.4 \\ \hline Caryophyllene oxide & 15.0 & 49.5 & 50.0–100.0 & 0.0347 & 0.1738 & 0.9947 & 10.2–16.5 & 18.8–30.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: LOD, LOQ, linear dynamic range, slope (a), x-intercept (b), and determination coefficient (\(r^{2}\)) values from the calibration plots obtained for the six target BVOCs under study and intra and inter-day precisions for HS-BA\(\mu\)E(CN1)/GC-MS assays under optimized experimental conditions.  
the homoscedasticity of the experimental data and validating the suitability of the linear regressions plotted for the analysis of the six BVOCs.  
The precision of the proposed methodology was evaluated by determining the RSDs using intra-day (\(n=5\)) and inter-day (\(n=3\), over 2 consecutive days) assays. Three different spiking levels were assessed, including low, medium, and high contents, i.e., 20.0, 40.0, and 100.0 \(\upmu\)g/L, respectively. In both intra-day and inter-day assays, the methodology demonstrated favorable RSDs across all studied spiking levels (4.0% \(\leq\) RSD \(\leq\) 30.1%), indicating its suitability for assessing the six BVOCs under investigation. Additionally, it was observed that intra-day precision yielded lower RSD values compared to inter-day precision, suggesting better repeatability in the obtained data than intermediate precision.