3.4.1. Fitting the Models

Experimental results of the responses, including the DPPH values and sensory characteristics of biscuits fortified with RPC, were fitted to the CCD, and the least-squares technique was used for calculation of the regression coefficients of the individual linear, quadratic, and interaction terms (Table 4).

**Table 4.** Regression coefficients of quadratic polynomial models for the studied response variables.


Significant at the \* *p* < 0.05; \*\* *p* < 0.01; \*\*\* *p* < 0.001.

The second-order polynomial equations generated were used to predict the responses (Tables 2 and 3). The ANOVA results for the predicted response quadratic models are listed in Table 5. ANOVA test revealed that the quadratic polynomial models adequately represent responses of DPPH for extracts obtained by conventional extraction and UAE as well as sensory properties due to an insignificant lack-of-fit (F ranged between 2.89 and 18.83, *p* > 0.05) for each estimated response (Table 5).

**Table 5.** Analysis of variance (ANOVA) results for the studied responses of biscuits: DPPHCE, DPPHUAE, color, odor, texture, flavor, overall acceptability, and purchase intent.


\* Significant at the *p* < 0.05 level; \*\* Significant at the *p* < 0.001 level; DPPH—2,2-diphenyl-1-picrylhydrazyl method; CE—methanolic extracts obtained by conventional extraction; UAE—methanolic extracts obtained by ultrasound-assisted extraction.

> Moreover, high F-values ranged between 154.89 and 1281.56, and the probability values less than 0.05 and 0.001 indicated that the empirical models were significant (Table 5). For this reason, these proposed mathematical models are valid and convenient for predicting the antioxidant potential and sensory properties of functional biscuits prepared under any combination of RPC amount and fat type.

Additionally, determination coefficients (R2) and adjusted R2 were calculated to estimate the proposed models' goodness of fit (Table 5). The R2 values (0.9664–0.9969) ensure a satisfactory fit of the proposed models to represent actual relationships between the responses (DPPHCE, DPPHUAE, color, odor, flavor, overall acceptability, and purchase intent) and the independent variables (RPC content and SAFA content). However, high values of adjusted R2 = 0.9328–0.9938 indicated a close agreement between experimental and predicted results. On the contrary, the values of R2 = 0.7751 and adjusted R2 = 0.5503 for the response of biscuits' texture suggest that a high proportion of variability cannot be explained by the model, because R2 should be at least 0.80 for a good fit.

All linear and quadratic parameters of the empirical models were highly significant (F = 19.73–4554.65, *p* = 0.00022–0.047) for the DPPH results of methanolic extracts obtained by conventional extraction and overall acceptability of the biscuits enriched with RPC, while the interaction between amounts of RPC and SAFA in functional biscuits produced a significant negative effect only on their odor (F = 66.85, *p* = 0.015). However, the quadratic parameter of the SAFA content and linear term of RPC of the models significantly influenced (F values ranged between 19.10 and 3221.88, *p <* 0.05) on flavor and purchase intent of the prepared biscuits. In addition, only two parameters (RPC and RPC2) had significant effects on color of the novel biscuits (F = 19.64–846.11, *p* = 0.047–0.0012). Both linear (RPC, SAFA) and quadratic (SAFA2) parameters of the models were highly significant (F = 27.44–1332.02 and *p* = 0.035–0.00075) for DPPH of methanolic extracts after UAE, whereas linear term of SAFA and interaction between independent variables (RPC × SAFA) caused insignificant effects (F = 0.00026–10.98, *p* = 0.080–0.99) on the texture of studied samples.

It is noteworthy that the variable with the largest positive effect on the antioxidant potential of the baked biscuits determined by DPPH assay was the linear term of RPC content (F = 1332.02–4554.65, *p* < 0.001). Nevertheless, this independent contributed variable the most negatively to all sensory characteristics of the fortified biscuits (F = 76.73–5902.97, *p* < 0.05).

#### 3.4.2. Analysis of the Response Surfaces

The effects of the two independent variables (amounts of RPC and SAFA) on antioxidant potential of biscuits extracted by classical extraction and analyzed by the DPPH assay as well as their five sensory characteristics (color, odor, flavor, overall acceptability, and purchase intent) were illustrated using surface response and contour plots of the quadratic polynomial models (Figure 2).

As can be seen, the generated shapes of the response surfaces for AC results differ from those obtained for sensory scores. The DPPH of baked biscuits significantly increased with the increasing concentration of RPC in the dough (Figure 2a). The parabolic shape of the response surface for DPPH was caused by the positive values of the quadratic terms of RPC amount and content of SAFA in the fat used.

On the contrary, scores for color, odor, flavor, and overall acceptability and purchase intent of the biscuits analyzed were the highest when RPC was not added to WF and rapeseed oil or coconut oil were used for dough preparation (Figure 2b–f). The surface plots of odor, flavor, overall acceptability, and purchase intent indicate that the negative linear of RPC content and positive quadratic term of SAFA content were significant (Figure 2c–f). The elliptical contour of the odor plot confirms that there was an interaction between independent variables (Figure 2c), whereas the significant negative linear and quadratic effects of RPC amount resulted in a decrease of the score for biscuit color after the fortification with a higher RPC amount (Figure 2b).

**Figure 2.** Response surfaces and contour plots for: (**a**) DPPH results of extracts obtained by conventional extraction (DPPHCE), (**b**) color, (**c**) odor, (**d**) flavor, (**e**) overall acceptability, and (**f**) purchase intent of functional biscuits expressed as a function of the rapeseed press cake (RPC) content and saturated fatty acids (SAFA) content.
