## 4 Numerical Results
### Discussion and Comparison of the Four MLR Models  
The performance measures of the developed MLR models (51)-(54) are summarized in Table 3. The graphical results of the models developed under the four outlier detection options (Op1-Op4) were presented in Figures 3-11 for each of the nine experimental groups of 14 records in the training set (as described in Section 2). Only the unitless wavelength (\(x_{1}=K\)) is changing within any of the groups, so the MLR was depicted as nine one-dimensional graphs. We can conclude the following:  
1. The experimental data given in Figures 3-11 contain no obvious pattern of hydrodynamic efficiency (\(y\)) dependency on the unitless wavenumber (\(x_{1}=K\)) even for the experiments in a single group. That shows that the problem of hydrodynamic efficiency prediction of OWC WEC is far from trivial. 2. Neither of the four developed models includes a regressor, which depends on the slope of the bottom, \(x_{i,5}=\theta\). That result supports the one reported in [34], but contradicts the predictions of the analytical model in [15]. Additional experimental work is needed to produce a training data set with a more balanced and diverse slope of the bottom values. 3. The four developed models use regressors depending on the unitless wavenumber (\(x_{1}=K\)), on the width of the chamber (\(x_{3}=B\)), and on the diameter of the orifice (\(x_{4}=D\)). All developed models, except the model (52) developed under Op2, include one or two regressors that depend on the submerged front wall length (\(x_{2}=d\)). Such a result is expected and shows that the stepwise regression algorithm, MSRA, has performed excellently in four setups determined by Op1, Op2, Op3, and Op4. Figure 4: The four models for Group 2. Figure 3: The four models for Group 1. Figure 5: The four models for Group 3. The outliers for a model are denoted above the point with a cross in a respective color. Figure 6: The four models for Group 4. Figure 8: The four models for Group 6. The outliers for a model are denoted above the point with a cross in a respective color. Figure 7: The four models for Group 5. The outliers for a model are denoted above the point with a cross in a respective color. Figure 10: The four models for Group 8. Figure 9: The four models for Group 7. 4. The holdout performance measures, based on the predicted residuals, were quite satisfactory for all of the four regressions (see Table 3) which proves the credibility of the developed MLR models for hydrodynamic efficiency prediction of OWC WEC. Figures 3-11 show that the data has high levels of inherited variability with low signal-to-noise ratio (SNR). We can see that the very elaborate model presented in [33] produced predictions not much better than ours because of the inherited variability. Even if a model fits all data points in its prediction, it is because the model reflects not the signal, but the noise in the data, which is a well-known problem of overfitting and a recipe for disaster in engineering. Very often, in engineering practice we consider models with \(R^{2}\) below 0.8 to be poorly specified. This assumption is not absolute but depends on the inherited variability in the data. Furthermore, \(R^{2}\) is an optimistic measure of performance, and it is better to be replaced by \(R^{2}_{HO}\). Even though there is no adopted practice for the \(R^{2}_{HO}\), the high values of \(R^{2}_{HO}\) (from 0.730 to 0.787) are particularly impressive. Figures 3-11 also show the lack of bias, which shows that most likely there are no missing variables in the models. Having in mind that those models would be utilized in the preliminary design, where their simplicity is as important as precision, the four developed models are rather useful. 5. Only five records from the training set have been identified as outliers: one observation (40) from all the three models, two observations (42 and 84) from two models each, and two observations (70 and 124) from a single model each.