## 3 Results and Discussion  
### Models Based on Data Miner Statistica  
When working with a problem formulated in this way, the learned ANN directly transforms the input data into output data by extracting the rules linking the output data to the input data during the learning process. This network does not calculate the outputs but estimates them in one pass, hence the more complex data structure. A network with a more complex hidden layer is needed for the estimation of the results. The best MLP network structure for solving the present task turned out to be a 5-8-1 MLP network, i.e., one with eight neurons in the hidden layer, with all activation functions in the hidden layer (Tanh), and the output layer being exponential (Table 2). This may indicate a significant non-linearity in the relationship between the input and output variables. The correlation coefficient \(r\) determined for the MLP network (Table 3) is calculated between the output variable and its prediction conducted by the network. It is a measure of whether the predicted values are consistent with the actual values of the dependent variable. It takes values in the range \(<\!-1\); \(1\!\!>\), where \"\(1\)\" means perfect compliance. The data used in the research are measurement results; they therefore contain a certain amount of metrological noise (also called \"dynamic noise\"). As such, the correlation coefficient calculated correctly for training cases should not be close to 1 (unless the noise is very weak). In the case of a very high \(r\), one may suspect that the network has been overfitted. This is a basic means of verifying the correct operation of the network. The predictions of an overtrained network will have an inflated correlation coefficient, compared to the values in the training sample. In this case, the network's prediction for data that it \"had not seen before\" during training was poor. Therefore, when choosing a network, its quality for the test and validation sets must be taken into account. A low (but not negative) correlation coefficient does not necessarily indicate the poor quality of the network, but it may reflect high noise levels in the data, which the network copes with as well as possible. The correlation coefficient \(r\), which, in this study, oscillates around the values presented in Table 3, indicates that the network has been trained correctly. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network Structure** & \
\begin{tabular}{c} **Activation Function Type** \\ **(Hidden Layer)** \\ \end{tabular} &
\begin{tabular}{c} **Activation Function Type** \\ **(Output Layer)** \\ \end{tabular} \\ \hline MLP 5-9-1 & logistics & Tanh \\ MLP 5-9-1 & Tanh & Tanh \\ MLP 5-6-1 & Tanh & linear \\ MLP 5-9-1 & logistics & linear \\
**MLP 5-8-1** & **Tanh** & **exponential** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Activation functions of the best MLP networks for the task described in the paper. The network with the best performance is shown in bold. In order to reliably assess the performance of the models, additional indicators describing their quality should be considered. For regression models, a commonly used measure is R\({}^{2}\), which is the percentage of variance in the dependent variable explained by the independent variables. R\({}^{2}\) takes values in the range <0; 1>, where 1 is the best-fitting value. In some calculation systems, R\({}^{2}\) may be negative, e.g., when the network does not reflect the trend of changes. The R\({}^{2}\) and RMSE values for the best MLP neural networks in the research are presented in Table 4.  
The root mean square error (RMSE) (also called the root mean square deviation or RMSD) measures the difference between the values predicted by the model and the values observed in the modeled environment. The RMSE is the square root of the squared loss, but it gives greater weight to larger differences. The mean square error is commonly used in forecasting and regression analysis to verify experimental results.