*3.1. Fitting the Experimental Data with the Models*

The matrix of the experimental design containing the 17 formulations generated by the software and the results achieved after performing all the experimental runs are summarized in Table 3.

For data fitting, the partial least squares (PLS) method was employed and several statistical parameters were further used to assess the fitting results. The coefficient of correlation (*R*2) represents the variation of the response explained by the selected model, or goodness of fit, while the Q2 indicates the model capacity to be predictive. Furthermore, ANOVA test was employed to assess the experimental model validity, significance and lack of fit. The model proved good predictive ability, as shown by Q<sup>2</sup> > 0.7, and a good correlation between the predicted and observed values was found, as suggested by *R*<sup>2</sup> > 0.9 (Table 4). Differences of less than 0.2–0.3 between *R*<sup>2</sup> and Q2 indicate a high predictive power of a good model. Models proved adequate validity (>0.4) corroborated with a reduced lack of fit for each evaluated response. The reproducibility values were >0.95, which means that the replicates generated similar responses by working under identical experimental conditions, thus making the experimental setup adequate for the purpose of the study. The results of ANOVA test showed a significant influence of the evaluated factors over TPC, TFC, CTC, and AA-TEAC, with *p*-value for the regression <0.001 (Table 4). Considering the results shown in Table 4, the fitting models were found to be appropriate to describe the experimental data, as the values for the lack of fit were not significant in extent with the pure error. The regression equation coefficients for the responses are presented in Table S4.



 stirring time; X2, pH; X3, water in solvent (%, *v*/*v*). TPC: Total phenolic content expressed as mg GAE/g dw = gallic acid equivalents per dry weight of hazelnut involucre; TFC: Total flavonoid content expressed as mg QE/g dw = quercetin equivalents per dry weight of hazelnut involucre; CTC: Condensed tannin content expressed as mg CE/g dw = catechin equivalents per dry weight of hazelnut involucre; AA-TEAC: Antioxidant activity by TEAC assay expressed as mg TE/g dw = Trolox equivalents per dry weight of hazelnut involucre. Data are shown as mean ±SD (standard deviation).


*p*-value, probability.

**Table 4.** Statistical parameters after data analysis and fit with factorial model.

The influence of the extraction conditions (factors) on the quantified individual compound levels (responses) was studied using the second experimental design during the optimization step (Table 2). The factors were the same as in the screening step and the responses were the levels of the 14 bioactive compounds (polyphenols and sterols) (Table 5). Moreover, the samples were hydrolyzed and the results of the recovery for the main bioactive compounds were compared to those obtained from non-hydrolyzed samples (Table S5). The statistical parameters *R*2, Q2, regression, lack of fit and pure error were determined for fitting the experimental data with the experimental design. The selected model presented good quality, with *R*<sup>2</sup> values between 0.75 and 0.94 and Q<sup>2</sup> results in the range of 0.47–0.84. For all the evaluated responses, the results of ANOVA test for the model had statistical significance (*p* < 0.05) and lack of fit *p*-values in the range of 0.064–0.91 (Table S6). Considering the values obtained for these statistical parameters, the experimental data for the bioactive compounds were adequately described by the fitting models, with a quadratic model statistically significant and a low lack of fit. The evaluated responses were significantly influenced by the chosen factors. The regression equation coefficients for all the bioactive compounds determined in HI extracts are shown in Table S7.



*Antioxidants* **2019** , *8*, 460

per gram of dry weight hazelnut involucre. ND—not determined.
