*3.1. Fitting of the Experimental Data with the Models*

The quantitative factors studied were the microwave power, with 4 levels of variation (300, 450, 600, 800 W) and the extraction time, varied over 3 levels (2, 3, 4 min). The total phenolic contents (TPCs) extracted with different solvent types (water, ethanol–water 50:50 and 80:20) were introduced in the DoE as 3 separate responses, which allowed a good comparison of their TPC extraction capacities.

As presented in Table 2, the design matrix calculated by the DoE software comprised 15 experimental runs, including three replicates that were used to confirm the experimental reproducibility, and to allow the identification of potential errors. Moreover, in order to reduce foreseeable results, the experimental runs were performed in a randomized order, dictated by the software. After performing all experimental runs, the registered response values were centralized and further introduced into the DoE matrix, where the fitting of the data has been accomplished by applying a multiple linear regression (MLR) algorithm. The fitting quality was evaluated by using the recommended, most reliable statistical parameters, i.e., the goodness of fit (R2), prediction capacities (Q2), model reproducibility given by the three performed replicates and model validity represented by the ANOVA test.


**Table 2.** Matrix of experimental design and experimental results for total phenolic content (TPC).

Notes: values with bold—outliers, TPC—total phenolic content expressed as mg GAE/g—gallic acid equivalents per dry plant material. BBE 1—extracts obtained with water 100%, BBE 2 extracts obtained with ethanol–water 50:50, BBE 3 extracts obtained with ethanol–water 80:20. Each value is the mean ± SD of three independent measurements.

Firstly, in order to improve the raw model by identifying and eliminating potential outliers, two graphs were generated for each response separately; the residuals plot (Figure 1a) which illustrates the residuals on a cumulative normal probability scale and the observed vs. predicted plot (Figure 1b) which allows the investigation of individual points that deviate from the diagonal line. By analyzing the two plots, outliers—marked with gray in Table 3, have been identified and eliminated, providing in this way an excellent fitted model, with high prediction capacities, as shown in the summary of fit chart (Figure 1c). In order to confirm the statistical validity of the model, the ANOVA test was performed (Supplementary file, Table S1). The registered *p* values were <0.001 for the model, describing a statistically valid design, indicating a significant impact of the factors on the responses. The *p* values registered for the lack of fit were > 0.099, showing that the model has insignificant lack of fit [27].

The generated coefficient plot (Figure 1d) allows the evaluation of factors' (independent variables) effects over the obtained responses, this type of diagram is used to evaluate the significance and influence of the model terms, each term or interaction being represented as a scaled and centered coefficient. In the present case, the diagram, shows that the extraction time varies inversely (for water 100%) or directly (for ethanol–water 50:50) with the amount of extracted TPC. The microwave power favors TPC extraction but in different proportions.

**Table 3.** Optimal extraction parameters, DoE predicted and experimental obtained values of the extracted TPC.


Notes: BBE 1—extracts obtained with water 100%, BBE 2—extracts obtained with ethanol–water 50:50, BBE 3—extracts obtained with ethanol–water 80:20.

**Figure 1.** Graphical summary of (**a**) residuals normal probability; (**b**) observed vs. predicted (**c**) summary of fit; (**d**) scaled and centered coefficients (TPC100—total phenolic content in extracts obtained with water 100%, TPC50/50—total phenolic content in extracts obtained with ethanol–water 50:50, TPC80/20—total phenolic content in extracts obtained with ethanol–water 80:20).
