## 4 Conclusions  
In this study, luteolin, caffeic acid, and apigenin were determined by HPLC-DAD and identified by UHPLC-Q-TOF-MS after UAE of a dry parsley sample. Then, a Box-Behnken design (BBD) was developed to optimize the extraction of these three phenolic compounds from _Petroselinum crispum_ (parley) by applying Box-Cox transformation of the data and model reduction. Determination of luteolin, caffeic acid, and apigenin in each set of experimental conditions was performed by HPLC-DAD.  
After data Box-Cox transformation and model reduction, the adequacy of the predictive model and the verification of the model were confirmed. Optimal conditions were calculated for each of the three phenolic compounds: 100 mL/g, 0% ethanol, 25 \({}^{\circ}\)C and 40 min for apigenin with predictive and actual values equal to 23.53 and 25.29 \(\pm\) 1.82 and value for desirability equal to 1.000; 20 mL/g, 0% ethanol, 70 \({}^{\circ}\)C and 40 min for caffeic acid with predictive and actual values equal to 18.48 and 19.10 \(\pm\) 0.75 and value for desirability equal to 1.000; and 100 mL/g, 40% ethanol, 70 \({}^{\circ}\)C and 40 min for luteolin with predictive and actual values equal to 24.54 and 23.92 \(\pm\) 1.86 and value for desirability equal to 0.9822.  
The three extracts acquired under the optimized conditions indicated for each compound of interest, namely caffeic acid, luteolin, and apigenin, presented similar behavior with respect to the total phenolic content and antioxidant activities based on FRAP and CUPRAC assays. Different composition of optimized extracts led to lower antioxidant activity of optimized extract for caffeic acid compared to those for luteolin and apigenin based on DPPH and ABTS assays. Satisfactory amounts of phenolic compounds (ranged from 38.8 to 39.9 mg GAE per g of dry parsley) were extracted and high antioxidant capacities (ranged from 13.2 to 687.8 nmol Trolox equivalent per g of dry parsley with respect to DPPH, ABTS, FRAP and CUPRAC assays) were obtained (Table 6).  
The results of the study highlight the nutraceutical potential of the parsley extracts. Parsley is an aromatic herb with widespread cultivation, and a considerable amount is easily accessible for the creation of novel functional foods or the refinement of current traditional products with shown superiority in consumer health protection.  
Conceptualization, H.C.K.; methodology, H.C.K., A.M., A.S.K., N.S.T. and M.E.D.; software, H.C.K. and A.M.; validation, H.C.K. and A.M.; investigation, H.C.K., A.M. and A.S.K.; resources, H.C.K., N.S.T. and M.E.D.; data curation, H.C.K. and A.M.; writing--original draft preparation, A.M.; writing--review and editing, H.C.K.; supervision, H.C.K.; project administration, H.C.K.; funding acquisition, H.C.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by EPAnEk-NRSF 2014-2020; Operational Program \"Competitiveness, Entrepreneurship and Innovation, Call 111 \"Support of Regional Excellence\" in the context of the implementation of the program: AGRICA II: AGrifood Research and Innovation Network of ExCellence of the Aegean, which is co-financed by the European Regional Development Fund (ERDF), MIS code: 5046750, and the APC was funded by the special account for research grants (SARG) of the University of the Aegean.  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.