Table 2.
Analysis of variance (ANOVA) for the response surface quadratic model.
| Source | Sum of Squares | df | Mean Square | F Value | p-value |
|---|---|---|---|---|---|
| Model | 45.29 | 14 | 3.24 | 229.64 | <0.0001 |
| X1: Temperature | 8.79 | 1 | 8.79 | 623.9 | <0.0001 |
| X2: Ethanol concentration | 0.035 | 1 | 0.035 | 2.5 | 0.1362 |
| X3: Time | 0.0048 | 1 | 0.0048 | 0.34 | 0.5687 |
| X4: Liquid-to-solid ratio | 10.53 | 1 | 10.53 | 747.33 | <0.0001 |
| X 1 X 2 | 0.027 | 1 | 0.027 | 1.93 | 0.1862 |
| X 1 X 3 | 0.068 | 1 | 0.068 | 4.8 | 0.0459 |
| X 1 X 4 | 0.1 | 1 | 0.1 | 7.27 | 0.0174 |
| X 2 X 3 | 0.023 | 1 | 0.023 | 1.6 | 0.2269 |
| X 2 X 4 | 0.017 | 1 | 0.017 | 1.2 | 0.2919 |
| X 3 X 4 | 0 | 1 | 0 | 0 | 1 |
| X 1 2 | 21.3 | 1 | 21.3 | 1512.04 | <0.0001 |
| X 2 2 | 0.089 | 1 | 0.089 | 6.32 | 0.0248 |
| X 3 2 | 0.61 | 1 | 0.61 | 43.09 | <0.0001 |
| X 4 2 | 7.37 | 1 | 7.37 | 523.14 | <0.0001 |
| Residual | 0.2 | 14 | 0.014 | ||
| Lack of Fit | 0.17 | 10 | 0.017 | 2.67 | 0.1785 |
| Pure Error | 0.026 | 4 | 0.00643 | ||
| Cor Total | 45.49 | 28 | |||
| Adeq Precision | 56.589 | ||||
| R2 = 0.9957; Adj R2 = 0.9913; Pred R2 = 0.9774 | |||||
ANOVA can fully reflect the significance and reliability of the response surface quadratic regression model [23,24]; as indicated in Table 2, the model was highly significant (F = 229.64, p < 0.0001). The p-value for the lack of fit was not significant (F = 2.67, p = 0.1785), which indicates the adequate predictive relevance of the model to explain the associations of independent variables with dependent variables. The linear coefficients (X1, X4), quadratic coefficients (X12, X22, X32, and X42), and interaction coefficients (X1 X3, X1 X4) were significant (p < 0.05). The R2 value of 0.9957 indicates a reasonable fit of the model to the experimental data. An R2 value (multiple correlation coefficient) closer to one denotes better correlation between the observed and predicted values. In this study, the values of R2 (0.9957), Pred R2 (0.9774), and Adj R2 (0.9913) indicate a good correlation between the experimental and predicted values, which shows that the model was significant. In addition, “Adeq Precision” (a measure of the signal-to-noise ratio) of 56.589 indicates an adequate signal. It can be concluded that the model was statistically credible and reliable.