## 3 Results
### Definitive--Screening Design (DSD)
#### 3.2.2 Quality Charts and ANOVA  
To attest the statistical significance of tested independent variables, Pareto chart of the standardized effects together with analysis of variance (ANOVA) at 95.0 confidence interval (95.0 CI) were run. Figure 2; Pareto chart, shows that DC and AD were the most influencing main effects, followed by the interaction of pH \(\times\) CT. The extent and the direction of the effect for each of the tested variables can be perceived from the regression equation, Equation (4). As revealed in Equation (4), and while DC has a positive impact on adsorption capacity, the AD is negatively impacting the response. Yet, and as per the regression model, pH has the highest magnitude (with a plus sign), an issue which is not reflected by the Pareto chart. This can be understood by comprehensively looking at the model where the interactions of pH \(\times\) DC and pH \(\times\) ST are negatively influencing the adsorption capacity, an issue that a bit diminishes the impact of pH.  
Residual plots (normal probability plot of residuals, histogram of residuals, residuals versus fit, and residuals versus order, not shown) were employed to test data (residuals') distribution, whether residuals are normally distributed with a constant variance, and whether residuals are independent of one another. Similar conclusions were obtained using the ANOVA testing, Table 5. The statistical significance of tested variables at 95.0 CI was confirmed by \(p\)-values \(<\) 0.05. Table 5 also shows that F-statistic is relatively large for the model, linear, and two-way interactions implying the statistical significance of the tested variables. On the other hand, F-value was small in case of ST and lack-of-fit with a \(p\)-value \(>\) 0.05, indicating that the suggested model properly describes the relationship between the response and the predictors.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **DF \({}^{*}\)** & **Adj SS \({}^{*}\)** & **Adj MS \({}^{*}\)** & \(F\)**-Value** & \(p\)**-Value** \\ \hline
**Model** & 8 & 25.6710 & 3.2089 & 27351.92 & 0.000 \\ \hline
**Linear** & 4 & 25.0458 & 6.2614 & 53371.41 & 0.000 \\ pH & 1 & 0.0096 & 0.0096 & 81.89 & 0.000 \\ AD & 1 & 12.7534 & 12.7534 & 10870.38 & 0.000 \\ DC & 1 & 12.2826 & 12.2826 & 104694.78 & 0.000 \\ ST & 1 & 0.0002 & _0.0002_ & _1.60_ & _0.222_ \\ \hline
**2-Way Interactions** & 4 & 0.6253 & 0.1563 & 1332.43 & 0.000 \\ pH\(\times\)DC & 1 & 0.0509 & 0.0509 & 434.13 & 0.000 \\ pH\(\times\)ST & 1 & 0.5227 & 0.5227 & 4455.67 & 0.000 \\ DC\(\times\)AD & 1 & 0.0758 & 0.0758 & 646.39 & 0.000 \\ AD\(\times\)ST & 1 & 0.0544 & 0.0544 & 463.88 & 0.000 \\ \hline
**Error** & 17 & 0.0020 & 0.0001 & & \\ _Lack-of-Fit_ & 7 & 0.0009 & 0.0001 & 1.12 & _0.419_ \\ Pure Error & 10 & 0.0011 & 0.0001 & & \\ \hline
**Total** & 25 & 25.6730 & & & \\ \hline \hline \end{tabular} \({}^{*}\): DF: Degrees of Freedom; Adj SS: Adjusted sums of squares; and Adj MS: Adjusted mean of squares. AD: Adsorbent dose (mg/50 mL); DC: Dye concentration (ppm); and ST: Stirring time (min.). Statistically insignificant variables appear _italic_.  
\end{table}
Table 5: Analysis of variance (ANOVA) for the transformed response.  
Figure 2: Pareto chart of standardized effects following response transformation. Adsorption capacity (\(q_{e}\), mg/g) is the measured response. Variables exceeding the reference line (red dashed line) are statistically significant.