## 3 Results and Discussion  
### Model Fitting and Statistical Analysis  
The effect of independent variables including ultrasonic power, sonication time, extraction temperature and ratio of water to raw material and their combinations on the extraction yield of polysaccharide from green pea pod was studied and optimized through central composite response surface methodology. The extraction yield of GPPP was varied from 4.45% to 7.08% (Table 1). Analysis of variance (ANOVA) was used to analyze the experimental data and the results are listed in Table 2. The most of the variation in the response could be explained through the regression equation due to the high model _F_-value (321.03 for polysaccharide extraction yield) and the associated low _p_-value (\(p<0.0001\)) which indicated the significance of developed model. The accuracy and good correlation between the response and the independent variables were clearly demonstrated by the coefficient of determination (\(R^{2}\)) and adjusted coefficient of determination (adj-\(R^{2}\)). In this model, the \(R^{2}\) and adj-\(R^{2}\) values were 0.996 and 0.993, respectively. Reproducibility and good reliability of the model was confirmed by the low value of coefficient of variance (0.97) [30]. In this study, the adequate precision (signal-to-noise ratio) was found to be >61 for the response, which indicates the best fitness of the developed model. The synergistic effect of the independent variables on the extraction yield was indicated by a positive sign of the coefficients, whereas an antagonistic effect was indicated by negative coefficients [32]. A second-order polynomial model (Equation (3)) was generated by applying multiple regression analysis to the experimental data to express the relationship between the independent variables and the response. The final equation obtained in terms of coded factors is given as follows:  
\[ \begin{split} Extraction\ yield&(\%)\\ &=6.91+0.34X_{1}+0.25X_{2}+0.35X_{3}+0.37X_{4}+0.076X_{1}X_{2}\\ &+0.033X_{1}X_{3}+0.11X_{1}X_{4}-0.13X_{2}X_{3}-0.047X_{2}X_{4}- 0.054X_{3}X_{4}\\ &-0.31X_{1}^{2}-0.20X_{2}^{2}-0.34X_{3}^{2}-0.30X_{4}^{2}\end{split}  \tag{3}\]  
where \(X_{1}\), \(X_{2}\), \(X_{3}\) and \(X_{4}\) are the coded variables for the ultrasonic power (W), sonication time (min), ratio of water to raw material (mL/g) and extraction temperature (\({}^{\circ}\)C), respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & **Sum of** & **Degree of** & **Mean** & **F-Value** & **\(p\)-Value** \\  & **Squares** & **Freedom** & **Squares** & & \\ \hline Model & 16.37 & 14 & 1.17 & 321.03 & \textless{}0.0001 \\ X\({}_{1}\)-Ultrasonic power & 2.12 & 1 & 2.12 & 582.38 & \textless{}0.0001 \\ X\({}_{2}\)-Sonication time & 1.12 & 1 & 1.12 & 306.04 & \textless{}0.0001 \\ X\({}_{3}\)-ratio of water to raw material & 2.25 & 1 & 2.25 & 618.74 & \textless{}0.0001 \\ X\({}_{4}\)-Extraction temperature & 2.52 & 1 & 2.52 & 690.65 & \textless{}0.0001 \\ X\({}_{1}\) X\({}_{2}\) & 0.09 & 1 & 0.09 & 25.53 & \textless{}0.0001 \\ X\({}_{1}\) X\({}_{3}\) & 0.01 & 1 & 0.01 & 4.64 & 0.0479 \\ X\({}_{1}\) X\({}_{4}\) & 0.20 & 1 & 0.20 & 54.35 & \textless{}0.0001 \\ X\({}_{2}\) X\({}_{3}\) & 0.29 & 1 & 0.29 & 78.56 & \textless{}0.0001 \\ X\({}_{2}\) X\({}_{4}\) & 0.03 & 1 & 0.03 & 9.91 & 0.0066 \\ X\({}_{3}\) X\({}_{4}\) & 0.04 & 1 & 0.04 & 12.69 & 0.0028 \\ Residual & 0.05 & 15 & 3.64 \(\times\) 10\({}^{-3}\) & 11.74 & \\ Std. dev. & 0.06 & \(R^{2}\) & & 0.99 & \\ Mean & 6.21 & Adj-\(R^{2}\) & & 0.99 & \\ CV\% & 0.97 & Pred-\(R^{2}\) & & 0.97 & \\ PRESS & 0.33 & Adequate & & & 61.85 \\ Signal-to-noise ratio & >61 & precision & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis of variance (ANOVA) for regression model of extraction yield.