## 4 Results
### Verification of Prognostic Properties of the Model  
The verification of the prognostic properties of a model is the process of evaluating how well the model can predict future events based on the data it was trained on. It is a very important step in the development of forecasting models, as it allows for the assessment of the model's effectiveness and the improvement of its results. In order to determine the forecasting reliability of the created model, the actual total delays of ships were compared with the delays calculated by the model for a given intensity.  
The presented computational model explaining the correlation between total delay and intensity, oversized ships, and ships with dangerous cargo, is afflicted with a significant forecasting error--ranging from \(-4\%\) to as much as 1600%--in relation to actual values (Table 15). This can be explained by the relatively small amount of collected observations and the number of examined objects. It should also be noted that the calculated model explains the ability to predict total ship delays with an accuracy of 88.5%, and the probability of its reliability is 95%  
In order to interpret the calculated costs, the time difference \(\Delta\)t was also expressed as a percentage (Table 15). This allows for a quick verification of the percentage underestimation or overestimation of the values of financial losses calculated by the model. Further verification of the model was carried out by taking into account the values of traffic intensity  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variables in Tested Equation [Units]** & **Coefficients Value** & **Standard Error** & \(p\)**-Value** \\ \hline Intercept & \(-2.737\) & \(2.214\) & \(0.24015\) \\ \hline Traffic intensity during tests & & & \\ with/without delay [\(\mathrm{ship/hour}\)] & \(21.651\) & \(4.852\) & \(0.000776\) \\ \hline One-way traffic (oversize vessels) & & & \\ [no of ships] & \(1.861\) & \(0.658\) & \(0.015257\) \\ \hline Dangerous goods [no of ships] & \(2.867\) & \(0.438\) & \(2.79\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 13: Multivariate regression statistical model for an intensity of \(0.52\) ships/h.  
\begin{table}
\begin{tabular}{l c} \hline \hline Expected intensity & \(0.52\) ship/h \\ \hline Expected number of oversized vessels & \(1\) \\ \hline Expected number of ships carrying dangerous goods & \(1\) \\ \hline
**Total delay** & \(13.3\) h \\ \hline
**Estimated cost** & USD 4250.8 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Results obtained by the statistical model for an intensity of \(0.52\) ships/h.  
\begin{table}
\begin{tabular}{l c} \hline \hline \multirow{2}{*}{**No.**} & **Intensity** & **No of Vessels** \\  & **Oversize** \\  & **Vessels** \\ \hline
1 & 0.17 & 1 & 0 \\
2 & 0.42 & 1 \\
3 & 0.42 & 1 \\
4 & 0.42 & 1 \\
5 & 0 & 2 \\
6 & 0.5 & 0 \\
7 & 0.58 & 2 \\
8 & 0.67 & 1 \\
9 & 0.83 & 0 \\
10 & 0.83 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Comparison of real and model-predicted total delay times.  
that were not used in the model creation process. This was done to test the predictive capabilities of the model in relation to unrealized data, i.e., intensities that did not occur during the research period of this study.  
An attempt to apply the model to intensities outside the scope of the research database (Table 16) showed values burdened with significant predictive error (model delay). This can be attributed to the presence of a linear relationship between traffic intensity and delays, resulting in very large predictive errors at high intensity values.  
The estimated model in its presented form is not able to successfully predict reliable values of total delays. To confirm the performance of the model, further studies should be conducted, taking into account a larger number of research objects, estimation error, and confidence intervals of dependent variable coefficients sampled to estimate the explained variable (total ship delays).