## 2 Results and Discussion  
### Optimisation of SPME Extraction Conditions  
SPME sorption is dependent among other parameters on the sample volume, and it has been observed that extraction efficiency is improved when the volume of HS in the vial is minimised [19]. However, the extraction efficiency of volatile compounds may show a non-linear relation toward the sample volume due to fiber overload. Hence, the sample mass of the sample was examined under four different quantities (1.000, 1.850, 3.000, and 4.000 g). As illustrated in Figure 1a, sample amounts of 1.850 and 3.000 g improved extraction efficiency. However, a further increase from 3.000 to 4.000 g of sample had a negative effect on the extraction efficiency, yielding an optimal sample amount of 1.850 g.  
For the optimisation of stirring, four different stirring speeds (100, 150, 200, 250, and 300 rpm) were evaluated. As shown in Figure 1b, after sample stirring at 250 rpm, no further improvement in extraction efficiency was observed. Hence, a stirring speed of 250 rpm was used for further experiments. Although included in the DOE-RSM optimisation as a studied factor, a preliminary screening experiment was performed to determine the behaviour of the most critical HS-SPME condition for EVOO analysis, which is extraction temperature. Selection of an appropriate extraction temperature is crucial to minimise the oxidation of the olive oil sample inside the SPME vial, preventing the release of unwanted oxidation components [20]. More specifically, in unheated or heated-at-a-lower-temperature (50 \({}^{\circ}\)C) olive oil samples, a higher content of alcohols, esters, and terpen has been observed compared to oils heated at higher temperatures; in the latter, higher amounts of aldehydes and carboxylic acids were found [21]. During oxidation off-flavor compounds produced due to fatty acid deterioration can be detected [22]. Consequently, the initially pleasant sensory characteristics of the oil attributed to compounds derived from the lipoxygenase (LOX) pathway eventually give way to unpleasant sensory attributes due to volatile compound deterioration. The screening of this parameter was performed by monitoring the total peak area of the selected components that are indicative of olive oil oxidation, while also monitoring components that are generally desirable according to the literature [21; 22; 23; 24]. The selected compounds that indicate increased oil oxidation and must be kept at a minimum during sample heating were heptanal, 2-heptenal, octanal, and 2,4-heptadiene1. The compounds that were selected as desirable for the analysis and contribute to its green odour notes [25] were 3-hexenal, (2\(E\))-hexenal, 2-hexene-1-ol, hexan-1-ol, and 1-penten-3-one. The study of extraction temperature showed an increase for both the desirable and undesirable oxidation components (Figure 1c). As indicated, there is a steep increase for the desirable components maximizing at around 55 \({}^{\circ}\)C, while the increase for the oxidation components appears to take place also around 55 \({}^{\circ}\)C, showing continuous increasing  
Figure 1: Influence of (**a**) sample amount, (**b**) stirring speed on total areas, and (**c**) extraction temperature on selected VOCs. (E + 08 = \(\times\) 10\({}^{8}\)). trend for the whole tested temperature range. This is in accordance with other related studies [13; 21], where extraction temperatures above 55 \({}^{\circ}\)C were not considered and were not studied as a means to avoid thermal volatile alterations and oxidative degradation of the olive oil. Regarding DOE-RSM optimization, a quadratic model including all linear terms, two-way interaction terms and second-order terms was fitted to the response data. The Multiple R-squared, Adjusted R-squared, \(p\)-value, and output of the Analysis of Variance (ANOVA) table for the model can be seen in Table 1.  
As indicated by the Multiple R-squared, Adjusted R-squared, and \(p\)-value, the quadratic model is a good fit to the data and is statistically significant.