## 2 Results and Discussion
### Method Validation
#### 2.1.3 Linearity, Limit of Detection (LOD) and Limit of Quantification (LOQ)  
Calibration is a common and important step in analytical methods. Preferably, the calibration range should be set so that most analyte concentrations fall near the range's center. Since we intended to develop and validate an analytical method to quantify the amoxicillin in various matrices (wastewater, tab), based on the previous studies [6; 41; 42; 43; 44], we established an optimal, large range of calibration from the LOQ to 100 ug/mL to be relevant for each investigated matrix. Moreover, the calibration curves were forced to go through the origin resulting in high accuracy at low concentrations, which is proven by the repeatability of the LOQ (Table 2). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Amox** & **Dox** \\ \hline retention time (min) & 1.72 & 5.23 \\ RSD of retention time (\%) & 0.65 & 0.58 \\ asymmetry factor & 1.31 & 1.52 \\ resolution & 1.92 & 6.43 \\ theoretical plates & 11,558 & 26,328 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the HPLC-DAD Method for the Simultaneous Determination of Amox and Dox. The linearity is defined as the ability of the method to attain test results that are directly proportional to the analyte concentration in samples within a specific range [47]. The linearity study was conducted for the calibration curves in the range of 10-100 ug/mL (Figure 3). Each concentration was injected three times and evaluated under identical conditions. For both analytes, the correlation coefficient R2 > 0.996 indicates a linear relationship between the concentration of the analyte and the peak area. ANOVA analysis for both analytes also evidenced that the regression model was statistically significant and envisaged the outcome variable (\(p\) < 0.05). Calibration curves were prepared in solvent and by spiking both matrices (capsules and wastewater). No significant difference was observed, permitting the use of the same calibration curve (in solvent) for the Amox and Dox analysis in both matrices. The different matrices used to prepare the calibration curves were analyzed previously with the HPLC-DAD method, and no Amox and Dox levels were detected. High values of the correlation coefficients (R2 = 0.9999) were also obtained for the determination of Amox in tablets [6,41] and water [42], and for Dox in tablets [33] and water [44] by HPLC. This study attended to decrease the detection (LOD) and quantification (LOQ) limits to as low as practically attainable while still achieving good accuracy and precision. The LOQ is expressed as the lowest concentration of an analyte that can be quantitatively measured with acceptable accuracy and precision, while the LOD is the concentration that can be detected, but not certainly quantified [47]. The noise level of the developed method was too small to calculate the LOQ and LOD based on the signal-to-noise ratio. Therefore, the LOQ (0.7 ug/mL for Amox and 1.0 ug/mL for Dox) and LOD (0.2 ug/mL for Amox and 0.3 ug/mL for Dox) were calculated as 10 times and 3.3 times, respectively; the standard deviation of the response for the lowest feasible analyte concentration in the range and the calibration curve's slope [46]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Analyte**} & \multicolumn{2}{c}{**Capsules**} & \multicolumn{2}{c}{**Wastewater**} \\ \cline{2-5}  & **Amox (ug/mL)** & **Dox (ug/mL)** & **Amox (ug/mL)** & **Dox (ug/mL)** \\ \hline
1 & 0.754 & 1.12 & 0.711 & 1.064 \\
2 & 0.712 & 1.05 & 0.728 & 0.981 \\
3 & 0.673 & 0.947 & 0.694 & 0.976 \\
4 & 0.684 & 0.935 & 0.683 & 0.937 \\
5 & 0.746 & 0.935 & 0.648 & 1.037 \\
6 & 0.709 & 1.10 & 0.624 & 0.907 \\ RSD (\%) & 4.54 & 8.61 & 5.73 & 6.00 \\ Recovery (\%) & 102 & 101 & 97.3 & 98.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Repeatability and Recovery for the LOQ of the HPLC-DAD Method for the Simultaneous Determination of Amox and Dox in Capsules and Wastewater. Figure 3: HPLC calibration curves of (**a**) Amox and (**b**) Dox standards.