# Optimizing the Sodium Hydroxide Conversion Using Regression Analysis in CSTR
## 4 Results and Conclusions  
The present study deals with the maximization of NaOH conversion using step-wise regression analysis in a CSTR. The dependency of temperature, volume, agitation rate, and feed rate on reactor performance was examined as well as the interaction outcome of the operating parameters. The agitation rate (X\({}_{2}\)) and feed rate (X\({}_{3}\)) proved to have an insignificant influence on the reaction conversion at a significant level of 5%. Consequently, the temperature (X\({}_{1}\)) and reaction volume (X\({}_{4}\)) were found to have a significant influence on the reaction conversion using step-wise regression. The temperature and volume dependence on steady state NaOH conversion were described by a polynomial model of 2 nd and 3 rd order. A maximal steady-state conversion equal to 63.15% was achieved. No further improvement was found in the reaction conversion with 3 rd order polynomial, so the 2 nd order polynomial was considered as the optimum reaction conversion model. It may be stated that 2 nd order regression polynomial model is adequate to represent the experimental data very well.  
The author is responsible for all the aspects of the manuscript. Author has read and agreed to the published version of the manuscript.  
This work was funded by the Deanship of Scientific Research, King Khalid University, Abha KSA, Grant number GRP/213/42 and APC was funded by GRP/213/42.  
Not applicable.  
The authors declare that they have no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Model**} & \multicolumn{2}{c}{**Unstandardized**} & \multicolumn{2}{c}{**Standardized**} & \multirow{3}{*}{**t**} & \multirow{3}{*}{**Sig.**} & \multicolumn{2}{c}{**95.0\% Confidence Interval for B**} \\ \cline{3-3} \cline{5-8}  & & **B** & **Std. Error** & & & & **Lower Bound** & **Upper Bound** \\ \hline \multirow{4}{*}{\(1\)} & (Constant) & \(-0.139\) & \(1.429\) & \(-0.097\) & \(0.924\) & \(-3.285\) & \(3.007\) \\ \cline{2-8}  & \(\text{X}_{1}\) & \(-0.044\) & \(0.043\) & \(-1.746\) & \(-1.017\) & \(0.331\) & \(-0.139\) & \(0.051\) \\ \cline{2-8}  & \(\text{X}_{4}\)\({}^{2}\) & \(-0.862\) & \(0.260\) & \(-4.616\) & \(-3.311\) & \(0.007\) & \(-1.435\) & \(-0.289\) \\ \cline{2-8}  & \(\text{X}_{4}\)\({}^{3}\) & \(0.705\) & \(0.281\) & \(4.197\) & \(2.503\) & \(0.029\) & \(0.085\) & \(1.324\) \\ \cline{2-8}  & \(\text{X}_{4}\text{X}_{1}\)\({}^{2}\) & \(0.001\) & \(0.000\) & \(2.393\) & \(1.247\) & \(0.238\) & \(0.000\) & \(0.001\) \\ \hline \hline \end{tabular}
\end{table}
Table 21: Coefficients of 3 rd order polynomial with two predictors.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Minimum** & **Maximum** & **Mean** & **Std. Deviation** & **N** \\ \hline Predicted value & \(0.280386\) & \(0.631567\) & \(0.493438\) & \(0.0694271\) & \(16\) \\ \hline Residual & \(-0.0895859\) & \(0.0484141\) & \(0.0000001\) & \(0.0354797\) & \(16\) \\ \hline Std. predicted value & \(-3.069\) & \(1.990\) & \(0.000\) & \(1.000\) & \(16\) \\ \hline Std. residual & \(-2.162\) & \(1.169\) & \(0.000\) & \(0.856\) & \(16\) \\ \hline \hline \end{tabular}
\end{table}
Table 22: Residuals Statistics for 3 rd order polynomial model with two predictors.