*3.3. Mathematical Model Analysis*

The ethanol productivity results presented in the last section were subjected to an analysis of variance to evaluate if the mathematical model was significant (Table 4). *p*-values lower than 0.0500 showed that the model is significant while a Fit-value of 107.40 indicates there is only a 0.01% of chance that a Fit-value this large could occur due to noise. Similarly, A, B, C, AB, BC, A<sup>2</sup> , B<sup>2</sup> model terms were statistically significant with *p*-values lower than 0.0006. Regarding the pure error, the Lack of Fit was considered as not significant with a Fit-value of 57.66 and a *p*-value of 0.0996. Thus, there is only a 9.96% chance that a Lack of Fit-value this large could occur due to noise.

In addition, the accuracy of the model and its ability to predict in the design space was verified by the close relationship between the predicted and the experimental values obtained for the ethanol productivity main response (Figure S2). The Predicted R<sup>2</sup> of 0.9436 was found to be in reasonable agreement with the Adjusted R<sup>2</sup> of 0.9846 since the difference was less than 0.2. A correlation between these two parameters was also confirmed by a coefficient of determination (R<sup>2</sup> ) of 0.9938 when conducting a linear regression of the predicted and the experimental data. The signal to noise ratio of 36.9494 ("Adeq Precision") was significantly higher than 4, indicating an adequate signal to navigate the design space. In addition, the very similar ethanol productivity of 15.4 and 15.3 g/L/d obtained for both centre points (run 12 and 16, respectively) confirmed the stability and the reproducibility of the results (Table 3).

**Table 4.** ANOVA table of CCD-RSM used to optimise the fermentation of diluted sugar beet molasses using *S. cerevisiae* yeast.


<sup>1</sup> *p*-values < 0.0500 represent significant model terms.
