# Optimizing the Sodium Hydroxide Conversion Using Regression Analysis in CSTR
## 3 Results and Discussion  
### Experimental Findings  
The outcomes of the experimental study [25] were considered for the design of experiments and these outcomes are listed as:  
* The steady state conversion with respect to sodium hydroxide raised with increased temperature. * The higher reactor volume leads to reduced Xa. * An increased stirrer rate from 70 to 150 rpm results in declined steady state NaOH conversion. * The increased reactants flow is attributed to a decrease in reaction conversion. An analysis was applied to determine the correlation amongst the predictors (X\({}_{1}\), X\({}_{2}\), X\({}_{3}\) and X\({}_{4}\)), and steady state conversion (X\({}_{\text{A}}\)) is presented (Table 2). The moderate positive correlation (r = 0.446) is revealed between conversion and temperature. The correlation coefficient between stirrer speed and steady-state conversion is 0.099, specifying that 1% variations in stirrer rate lead to 9.9% variation in NaOH conversion. Low negative correlation (r = \(-\)0.076) was observed between feed rate and conversion, which states that \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **N** & **Range** & **Minimum** & **Maximum** & **Mean** \\ \hline Temperature, X\({}_{1}\) (\({}^{\circ}\)C) & 16 & 15 & 25 & 40 & 30.63 \\ Agitation rate, X\({}_{2}\) (rpm) & 16 & 120 & 70 & 190 & 130.00 \\ Feed flow rate, X\({}_{3}\) (mL/min) & 16 & 30 & 50 & 80 & 61.25 \\ Reactor volume, X\({}_{4}\) (L) & 16 & 0.75 & 1.00 & 1.75 & 1.4688 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Operation variables. conversion increases with reduced feed flows. Moderate positive correlation (r = 0.599) was observed between volume and conversion, which states that 100% increase in volume results in 59.9% surge in reaction conversion. It is realized that correlation is substantial at 0.05 significance level. An attempt was made to develop a regression equation model to optimize reaction conversion. The X\({}_{\text{A}}\) was assumed as a process response variable (dependent variable) and X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), and X\({}_{4}\) are the predictors. A SPSS tool was used to enter all the dependent and independent variable entered into model. Equation (5) was established to augment the steady state conversion of NaOH. \[\text{X}_{\text{A}}=\beta_{\text{o}}+\beta_{1}\text{X}_{1}+\beta_{2}\text{X}_ {2}+\beta_{3}\text{X}_{3}+\beta_{4}\text{X}_{4}+\text{e} \tag{5}\]  
X\({}_{\text{A}}\): predicted variable; X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), and X\({}_{4}\) are the predictors. All beta terms are the coefficient of predictors and \(\beta_{\text{o}}\) is an intercept of the developed model, which is a constant parameter. The symbol e signifies an error term of the developed model. As illustrated in Table 3 Model Summary, moderate positive correlation was observed between the dependent and independent variable. R square demonstrates that the goodness of fit is moderate, whereas adjusted R\({}^{2}\) explains an extraordinary influence of the extraneous variable. F value, as depicted in model summary Table 3, explains that the influence of independent variables varies considerably at 0.05 significance level. The \(p\)-value less than 0.05 demonstrates that influence of independent variables varies significantly with 95% confidence interval as explained in Table 4. The tabulated F value is lower equated with the calculated one and recommends that independent variables variances of contribution are statistically substantial. It can also be concluded from the calculated sig. value presented in Table 5 (0.048) that the researcher is not fully confident about the variation of contribution of all predictors.