## 4 Discussion
The \(R^{2}_{prediction}\) was reserved for assessing the model's predictive ability. The obtained fitting results (\(R^{2}_{prediction}\)) was 89.75%, indicating that the model can explain approximately 90% of the variability observed in the test data for prediction and to evaluate the model's predictive capacity. Therefore, at this point, it is crucial to explain the combined role of the variables involved in the heat-treatment process and the resulting ultimate tensile strength values in terms of the specific characteristics of this alloy. Increasing the solutionizing temperature to 540 \({}^{\circ}\)C allows more alloying elements, such as Mg, Si, and Cu, to remain in a solid solution [10; 45]. Subsequently, these elements precipitate during artificial aging at high temperatures to form the Mg\({}_{2}\)Si (\(\beta\)) phase [3; 17]. In a study on various 6 XXX-type alloys, [PERSON] and [PERSON] [36] determined that tensile strength in such alloys is influenced by the amount of Mg and Si present in a supersaturated solution, with Mg\({}_{2}\)Si being the primary strengthening phase. The reinforcement of the tensile strength of the alloy after the heat-treatment process can also be attributed to the movement of dislocations due to the presence of foreign particles from any other phase. However, if the temperature increases, as observed in run 7, with aging at 170 \({}^{\circ}\)C and a solutionizing temperature of 540 \({}^{\circ}\)C, when we relate hardness to tensile strength, samples treated at 530 \({}^{\circ}\)C exhibited lower hardness. This is reflected in decreased tensile strength or strengthening due to the coalescence of precipitates within a larger particle. Additionally, the annealing of defects occurs, which causes a reduction in obstacles to the movement of dislocations. Ternary systems like Al-Mg-Si and alloys without an excess of Si exhibit a well-established precipitation sequence, as was demonstrated in previous studies using transmission electron microscopy (TEM) [37; 46]:  
* Solid solution
* GP (Guinier-Preston) zones
* Needle-shaped precipitates aligned with the (100) direction of the matrix and coherent with the Al matrix along their major axes
* \(\beta^{\prime}\) phase (rod-shaped precipitates, semi-coherent with the matrix)
* \(\beta\) phase (Mg\({}_{2}\)Si, plate-shaped equilibrium precipitates)  
This sequence illustrates the compositional changes during precipitation, contributing to understanding the alloy's mechanical properties. It is worth noting that numerous studies in the literature have effectively utilized TEM to explain the microstructural evolution during aging treatments. Notably, research compiled by [PERSON] [5] has provided comprehensive insights into the transformation sequence, including observing GP zones and the evolution of the beta phase through applying TEM. Additionally, references such as those by [PERSON] [11], [PERSON] [6], and [PERSON] [47] have extensively investigated the phenomenon of beta dissolution utilizing TEM techniques, further supporting the efficacy of TEM in studying microstructural evolution during aging treatments. These findings align with the precipitation sequence previously reported [6; 15]: super-saturated solid solution (SSSS) \(\rightarrow\) Si/Mg clusters \(\rightarrow\) Guinier-Preston (GP) zones \(\rightarrow\)\(\beta^{\prime\prime}\rightarrow\)\(\beta^{\prime}\rightarrow\)\(\beta\). Despite recrystallization (during the solutionizing stage), the \(\beta\) phase is still evident in the alloy after the thermal treatment, as we observed by XRD examination. The \(\beta\) phase is known for its strengthening effect on aluminum alloys, as it precipitates from the supersaturated solid solution during aging. The indexation of the diffraction peak at (220) confirms the existence of the \(\beta\) phase in the alloy (see Figure 9). It is worth noting that the morphology of \(\beta\) can vary, and in this alloy, it appears to exhibit plate-like or needle-likeshapes (see Figure 5).