## 1 _Application_
Overfitting may result in an ANN model trained over the uncertainties of the observations instead on their useful signal. It is typical of problems with small to medium dataset [10]. A wide variety of regularization techniques [27] and cross validation procedures [28] are developed to reduce the overfitting in ANN, some of them achieving great results. The training of an ANN is a random hyper-dimensional optimization process which takes a long time to train. As a by-product the predicted residuals described in Section 3.1 are rarely calculated in practical problems. However, the main shortcoming of an ANN prediction is the unreliable prediction for any input absent in the training or testing sets. Evidently, ANN is a great tool that constantly evolves, yet its use requires a very high level of expertise, which is often absent with engineering designers. The MLR method is by far the best-known BB model, with numerous applications to develop predictive models in various engineering tasks (see [29; 30; 31]). It uses approximation function of multiple variables which is linear according to the unknown parameters. Given a known dataset, the construction of an MLR predictor is very cheap and extremely fast in comparison with the other methods. It also provides a measure of the uncertainty in its prediction. On the negative side, although in most cases the precision of MLR models is enough for engineering purposes, it is as a rule lower than that of the ANN models [32]. However, the main shortcoming of MLR models is that their quality depends on the validity of several restrictive assumptions, which rarely hold in their entirety in any practical application. The actual popularity of MLR in engineering practice is not properly reflected in recent published works, where such models are utilized most often as a basic benchmark. As a result, more and more engineering practitioners tend to use methods they are not fully familiar with and with assumptions that are often violated. The MLR is a useful tool in a variety of problems, yet it should not be used in its basic form that may generate unreliable results as the assumptions are violated (see Section 3.2 for more discussion). In this paper, we shall develop a reliable and cost-effective MLR prediction of the hydrodynamic efficiency of the OWC as a function of the construction parameters using an existing data set. Such a model would be useful in the preliminary stages of design of WECs, but its reliability strongly depends on the validity of the classical linear regression assumption. We will introduce a series of novel/modified methods for assumption diagnostics that share two features: the repeated application of an improved singular value decomposition (SVD) of the design matrix using novel classification of the singular values, and the universal use of the predicted residuals. We shall propose: a novel procedure for reliable identification of the zero singular values of a matrix; a modified algorithm for stepwise regression; a modified algorithm to detect heteroskedasticity and identify statistically significant but practically insignificant heteroscedasticity in the original model; a novel test of the validity of the nullity assumption; a modified Jarque-Bera Monte Carlo error normality test; and a novel multiple testing outlier procedure with two phases in each cycle. We will investigate the correct placement of the outlier detection in the overall diagnostic sequence empirically. A new family of goodness-of-fit measures and the aforementioned outlier detection procedure are also based on predicted residuals. We will use predicted residual based modified performance indicators to demonstrate that the developed MLR model can produce highly reliable predictions of the OWC WEC hydrodynamic efficiency, provided that the construction and diagnostic procedures are modified to reflect the latest advances in statistics.