## 5 Conclusions  
An achievement of the paper is that we developed a cost and time effective MLR model, which is very useful in the preliminary stages of design of WECs. Our model utilized an existing experimental data set to reliably predict the hydrodynamic efficiency of an oscillating water column (OWC) with satisfactory accuracy. The reliability of the model is mostly due to the novel assumptions of the diagnostic algorithms that were proposed and applied in the described case study. More specifically, our work introduced several new/modified procedures, based mainly on predicted residuals and SVD:  
(1) PCCSV (Algorithm 1) is a novel procedure for reliable identification of the zero singular values of any matrix.  
(2) MSRA (Algorithm 2) is a modified algorithm for stepwise regression execution in three phases with balanced treatment of the constant term. It explicitly applies the improved SVD decomposition procedure and implicitly uses the predicted residuals (by utilizing \(t\)-tests with robust HC\({}_{3}\) estimator of the parameters covariance matrix, which is based on predicted residuals).  
(3) MHTRA (Algorithm 3) is a modified algorithm which deals with the heteroskedasticity by constructing better auxiliary regression and identifies practically insignificant heteroscedasticity in the original model. It explicitly applies the improved SVD decomposition procedure three times and it explicitly uses predicted residuals several times.  
(4) We proposed a novel test of the validity of the nullity assumption based on predicted residuals.  
(5) We modified the Jarque-Bera test for error normality where the \(p\)-value is derived by a Monte-Carlo procedure (Algorithm 4). It explicitly applies predicted residuals.  
(6) We developed and investigated the performance of four options for the placement of the applied outlier procedure CODPA (also using predicted residuals) in the overall diagnostic sequence and although the results were inconclusive, the different algorithms produced surprisingly stable predictions of the hydrodynamic efficiency of the OWC WEC devices.  
As a future development, we will concentrate on four different research directions. The first one is to apply the developed procedure on several new data sets to clarify the questions with dubious answers in the present paper. The second direction is to improve continuously the proposed algorithms. One possibility could be to develop more precisely the WLS model in MHTRA. Another possibility is to try improving MSRA by utilizing \(t\)-tests with the promising robust HC\({}_{4}\) estimator of the parameters' covariance matrix, as advocated in [42]. The third direction of future research is to modify the presented algorithms to deal with time series problems instead of only problems with cross-sectional data. That is a challenging task because in such problems the correlation assumption must be tested and relaxed with a cutting-edge procedure. Additionally, the right place of such a procedure in the overall diagnostic sequence needs empirical justification which is by no means trivial as the question for the proper placement of the applied outlier procedure CODPA will be readdressed. The fourth one refers to the application area of our procedures. The OWC device we selected was an illustrative example for the newly developed MLR procedures. However, the developed models produced promising hydrodynamic performance results.  
In future studies, we will attempt to apply the methodology to other types of WEC, such as absorbers, overtopping devices, etc.  
Conceptualization, K.T. and N.N.; methodology, K.T. and N.A.; software, K.T. and N.N.; validation, N.A. and H.A.; investigation, N.A. and H.A.; data curation, N.A. and H.A.; writing-- original draft, N.N. and N.A.; writing--review and editing, K.T. and N.N.; visualization, K.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.