## 4 Conclusions  
This work demonstrates the relevance of experimental design and method validation. Indeed, it goes further, by linking the two components and applying them to the analysis of VMSs in water. The application of design of experiments (DOE) enabled the study of the effect of input variables (factors) on an output variable (response) using the minimum number of experiments possible, thus saving time and resources. The developed HS-SPME technique emerges as an interesting solution to conventional procedures since it combines the potential to eliminate solvent consumption and the concomitant issues of used solvent disposal, with a simple, low-cost, and eco-friendly extraction procedure. In terms of performance parameters, the developed HS-SPME method presents similar results to those obtained by other studies found in the literature that also used HS-SPME for the analysis of VMSs in water samples. The present work also has the advantage of using a simple and cheaper instrumental methodology based on GC-FID, which is more easily replicable in WWTP analysis laboratories, to screen a larger number of samples. **Supplementary Materials:** Table S1: Factors and values for the proposed central composite design); Table S2: Proposed central composite design); Table S3: Second-order polynomial equation obtained for each target compound and model suitability parameters for the response functions; Table S4: Results from the Student's \(t\)-test for the main, quadratic and interaction effects; Table S5: Additional testing to prove the applicability of the proposed empirical model; Figure S1: Optimal conditions and desirability function; Figure S2: Chromatogram of a 3 \(\mu\)L\({}^{-1}\) calibration standard (A) and wastewater sample (B). **Author Contributions:** Conceptualization, F.B., V.H. and A.A.; methodology, F.B., V.H. and A.A.; software, F.B. ; validation, F.B., V.H. and A.A.; formal analysis, F.B. and P.G.-H.; investigation, F.B. and P.G.-H.; resources, A.A, V.H., N.R. and V.P; data curation, F.B. ; writing--original draft preparation, F.B. ; writing--review and editing, A.A., V.H., N.R. and V.P. ; visualization, F.B. ; supervision, A.A., V.H., N.R. and V.P. ; project administration, V.H. and A.A.; funding acquisition, A.A, V.H., N.R. and V.P. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was financially supported by: (i) Base Funding--UIDB/00511/2020 of the Laboratory for Process Engineering, Environment, Biotechnology and Energy--LEPABE--funded by national funds through the FCT/MCTES (PIDDAC). ; (ii) Project PTDC/ASP-PLA/29425/2017--POCI-01-0145-FEDER-029425 and Project PTDC/CTA-AMB/32084/2017--POCI-01-0145-FEDER-032084 --funded by FEDER funds through COMPETE2020--Program Operacional Competitividade e Internacionalizacao (POCI) and by national funds (PIDDAC) through FCT/MCTES; (iii) PhD Grant PD/BD/137758/2018--[PERSON], supported by FCT PhD programme, under the Portugal 2020 Partnership Agreement and European Social Fund (ESF); (iv) National funds through FCT--Fundacao para a Ciencia e Tecnologia, I.P., under the Scientific Employment Stimulus--Individual Call--CEECIND/00676/2017 ([PERSON]); (v) [PERSON] thanks FCT for the financial support of his work contract through the Scientific Employment Stimulus--Institutional Call--CEECINST/00049/2018;(vi) [PERSON] thanks the Agencia Canaria de Investigacion, Innovacion y Sociedad de la Informacion (ACIISI), co-funded by the European Social Fund, for her FPI PhD fellowship; (vii) [PERSON] acknowledges funding from the Spanish Ministry of Economy (MINECO) project MAT2017-89207-R and also funding from the Canary Agency of Research and Innovation (ACIISI) project ProID2020010089. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study is available on request from the corresponding author. **Conflicts of Interest:** The authors declare no conflict of interest.