## 4 Conclusions  
Response surface methodology turned out to be an effective mathematical and statistical tool for modeling and optimizing the extraction process of bioactive compounds obtained from a coffee bean roasting by-product such as coffee silverskin. This technique enables not only the selection of the most favourable conditions for the extraction process, but also the obtaining of extracts with both a high content of bioactive compounds and antioxidant activity while performing a significant reduction in the number of experiments. Furthermore, response surface methodology allowed the significance of the effect of each extraction process independent variables and their interactions on the spectrophotometric and chromatographic methods used as responses to be determined. Among the examined process variables, the ratio of volume solvent to sample solid matrix and the concentration of used extractant are the most crucial factors affecting the extraction recovery yield of bioactive compounds from coffee silverskin. In accordance with the experimental data, the extraction with the use of 50% ethanol and the ratio of solvent volume to a sample matrix of 45:1 (\(v/w\)) for 30 min at 60 \({}^{\circ}\)C is the most promising variant of the process of extracting bioactive compounds from coffee silverskin. The ethanolic extract generated with the best variant of the extraction process could be considered a valuable source of caffeine (approx. 6.8 mg/g d.m. of the coffee silverskin) and phenolic compounds, including chlorogenic acids, with the content reaching 0.45 mg/g d.m. of the coffee silverskin sample. Additionally, the ABTS and FRAP assays revealed that this extract is characterized by high antioxidant activity (approx. 100 mmol Trolox/g d.m. of the coffee silverskin and approximately 180 mmol Fe(II)/g d.m. of the coffee silverskin, respectively). Taking the obtained findings into consideration, coffee silverskin can be proposed as a low cost and relatively stable waste plant material containing bioactive compounds with high antioxidant activity, which creates an opportunity for its valorization and innovative utilization approaches towards this potential environmentally harmful waste. Moreover, the authors would like to recommend that further experimental investigations will need to be conducted to evaluate the possibility of the implementation of coffee silverskin ethanolic extracts in liquid or powdered form as an ingredient of functional food products or biodegradable (packaging) materials used in the food industry.  
Conceptualization, R.B. and A.G.; methodology, R.B., A.G. and M.W.-W.; software, R.B.; validation, R.B., A.G. and M.W.-W.; formal analysis, R.B.; investigation, R.B.; data curation, R.B.; writing--original draft preparation, R.B.; writing--review and editing, A.G., M.W.-W. and I.P.; visualization, R.B. and I.P.; supervision, A.G. and M.W.-W.; project administration, R.B. and A.G.; funding acquisition, A.G. All authors have read and agreed to the published version of the manuscript.  
The study was financially supported by sources of the Ministry of Education and Science within funds of the Institute of Food Sciences of Warsaw University of Life Sciences (WULS), for scientific research.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tested RSM Response** & **Approximated Value** & **Actual Value** & **Deviation [\%]** \\ \hline ABTS [\(\mu\)mol Trolox/g CS d.m.] & 101.86 & 101.6 & \(-\)0.25 \\ FRAP [\(\mu\)mol Fe(II)/g CS d.m.] & 131.96 & 132.3 & 0.25 \\ TPC [\(\mu\)mol GAE/g CS d.m.] & 50.86 & 52.3 & 2.83 \\ BI (Abs/g) & 0.30 & 0.29 & \(-\)3.33 \\ Caffe [mg/g CS d.m.] & 6.04 & 5.9 & \(-\)2.32 \\
3-CQA [mg/g CS d.m.] & 0.21 & 0.22 & 4.76 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Verification of the mathematical models of the tested RSM responses—approximate values predicted by statistical analysis according to the fitted models and actual values of validation tests.