The adequacy of the model was checked with ANOVA which was tested by Tukey‘s statistical analysis (Table 2). The F-value and p-value of the lack of fit were 1.07 and 0.457 respectively, implying an insignificant difference relative to the pure error and a good fitness of the model. Coefficient of determination (R2) is defined as the ratio of the explained variation to the total variation,and R2 = 0.954 approaching unity suggested a good relevance of the dependent variables in the model. The adjusted determination coefficient of the model (R2 adj = 0.892) confirmed that the model was significant, indicating a good degree of correlation between the actual values and the predicted values of total oligosaccharides.The coefficient estimates of the model equation, along with the corresponding F-values and p-values are presented in Table 2. The p-value is used as a tool to check the significance of each coefficient,and also indicates the interaction strength between each independent variable. A small p-value indicates a more significant coefficient [34]. It can be seen that X1, X3, X1 2 , X2 2 , and X3 2 were significant model terms.The effect of solvent concentration, extraction time and temperature for UAE on the concentration of extracted total oligosaccharides is shown in Fig. 2. The relationship between independent and dependent variables is illustrated by three-dimensional representation of the response surfaces and the two-dimensional contours generated by the model.Two variables within the experimental range are depicted in three-dimensional surface plots when thethird variable is kept constant at zero level. From these threedimensional
profiles, the interactions between any two factors can be easily observed. The shapes of the contour plots, elliptical or circular, indicate whether the interactions between the corresponding variables are significant or not [19]. An elliptical contour plot means the interactions between the variables are significant while a circular contour plot means otherwise. Ethanol concentration had a high impact on the concentration of extracted oligosaccharides.Higher amount of oligosaccharides was extracted by ethanol concentration ranging from 52% to 66% v/v, temperature range of 35–50 C (Fig. 2A), and ultrasound time between 9 and 13 min (Fig. 2B). Increase in the oligosaccharide concentration was observed when extraction time and temperature were kept at their middle values (Fig. 2C). From the Fig. 2A–C, maximal concentration of oligosaccharides could be obtained at optimal value between every two factors. All parameters showed significant quadratic effect; time and temperature at p < 0.05 while ethanol concentration at p < 0.005 (Table 2).