## 3 Experiment Procedure
### Regression Analysis of Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multicolumn{6}{c}{\(\hat{Y}_{1}\)} & \multicolumn{6}{c}{\(\hat{Y}_{2}\)} \\ \cline{2-10}  & **Sum of Squares** & **df** & **Mean Square** & **\(F\) Value** & **\(p\)-Value Prob \(>F\)** & **Sum of Squares** & **df** & **Mean Square** & **\(F\) Value** & **\(p\)-Value Prob \(>F\)** \\ \hline Model & 0.60 & 14 & 0.043 & 26.58 & \textless{}0.0001 & 0.78 & 14 & 0.055 & 43.71 & \textless{}0.0001 \\ \(X_{1}-P\) & 0.18 & 1 & 0.18 & \textless{}0.0001 & 0.33 & 1 & 0.33 & 260.20 & \textless{}0.0001 \\ \(X_{2}-F\) & 0.18 & 1 & 0.18 & \textless{}111.18 & \textless{}0.0001 & 0.16 & 1 & 0.16 & 124.49 & \textless{}0.0001 \\ \(X_{3}-V_{5}\) & 0.055 & 1 & 0.055 & 34.45 & \textless{}0.0001 & 0.042 & 1 & 0.042 & 32.96 & \textless{}0.0001 \\ \(X_{4}-V_{7}\) & 0.050 & 1 & 0.050 & 30.95 & \textless{}0.0001 & 0.050 & 1 & 0.050 & 39.07 & \textless{}0.0001 \\ \(X_{3}X_{2}\) & 0.023 & 1 & 0.023 & 14.52 & 0.0017 & 0.026 & 1 & 0.026 & 20.91 & 0.0004 \\ \(X_{1}X_{3}\) & 0.012 & 1 & 0.012 & 7.77 & 0.0138 & 0.014 & 1 & 0.014 & 11.13 & 0.0045 \\ \(X_{1}X_{4}\) & 0.001743 & 1 & 0.001743 & 1.09 & 0.3141 & 0.02043 & 1 & 0.002943 & 2.32 & 0.1483 \\ \(X_{2}X_{3}\) & 0.004128 & 1 & 0.004128 & 2.57 & 0.1298 & 0.01463 & 1 & 0.001463 & 1.35 & 0.2995 \\ \(X_{3}X_{4}\) & 0.003221 & 1 & 0.003221 & 2.00 & 0.1772 & 0.003278 & 1 & 0.003278 & 2.59 & 0.1286 \\ \(X_{3}X_{4}\) & 0.0001051 & 1 & 0.000151 & 0.0065 & 0.0016 & 0.0001806 & 1 & 0.0001806 & 0.014 & 0.9055 \\ \(X_{4}\) & 0.0011 & 1 & 0.011 & 6.72 & 0.0204 & 0.005273 & 1 & 0.005273 & 4.16 & 0.0594 \\ \(X_{2}^{2}\) & 0.020 & 1 & 0.020 & 12.34 & 0.0031 & 0.028 & 1 & 0.028 & 22.28 & 0.0003 \\ \(X_{3}^{2}\) & 0.021 & 1 & 0.021 & 12.77 & 0.0028 & 0.029 & 1 & 0.029 & 23.14 & 0.0002 \\ \(X_{4}\) & 0.0005104 & 1 & 0.0005104 & 0.32 & 0.5813 & 0.002048 & 1 & 0.002048 & 1.62 & 0.2230 \\ Residual & 0.024 & 15 & 0.001606 & & 0.019 & 15 & 0.001267 & & & \\ Lack of Fit & 0.023 & 10 & 0.002296 & 10.06 & 0.0100 & 0.018 & 10 & 0.001815 & 10.66 & 0.0088 \\ Pure Error & 0.001141 & 5 & 0.0002282 & & 0.0008513 & 5 & 0.0001703 & & & \\ Cor Total & 0.62 & 29 & & 0.79 & 29 & & & & \\ \hline SD = 0.040, Mean = 0.076, C.V.\(\approx\) = 52.46, PRESS = 0.082, & SD = 0.036, Mean = 0.14, C.V.\(\approx\) = 24.69, PRESS = 0.063, & & & & \\ \(R^{2}\) = 0.9612, Adj = 0.9251, Pred = 0.9676, & & \(R^{2}\) = 0.9761, Adj = 0.9537, Pred = 0.9204, & & & & \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{}{} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} \\ \hline \end{tabular}
\end{table} 
Table 6: ANOVA for the response surface quadratic model of \(\hat{Y}_{1}\).