# Analysis of Instantaneous Energy Consumption and Recuperation Based on Measurements from SORT Runs
## 4 Discussion  
The learning time for the linear model was 0.0027 s, for the KNN it was 0.0024 s, and for the neural network it was 53.64 s. On the validation set, predictions were made for each of the models. Additionally, the expected time to estimate prediction per record for NN is decidedly higher, 0.00065 s, while the expected prediction time for the linear model is 0.00006 s and for KNN is 0.00009 s. Below (in Table 8 and Figure 10), the analysis of model predictions based on the validation set will be presented. For each of the models, validation was performed on the test set. The graphical fit of the models is presented in the Taylor diagram. The polar diagram shows the correlation coefficient between the actual and predicted values of the dependent variable and the standard deviation of the predicted values of the dependent variable for each model. The position of the linear model on the Taylor diagram is marked with a red square, for KNN a green triangle, and for NN a blue circle. The standard deviation for ICRE on the test set is 15.2416, and a black circle is marked on the standard deviation axis (which corresponds to the position of the perfect model).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test** & **Statistics** & \(\boldsymbol{p}\)**-Value** \\ \hline Shapiro–[PERSON] normality test & 0.8243954 & \(<2\times 10^{-16}\) \\ [PERSON]–[PERSON] test & 18.4066936 & \(<2\times 10^{-16}\) \\ Cramer–[PERSON] test & 3.5697818 & \(<2\times 10^{-16}\) \\ Lilliefors (Kolmogorov–Smirnov) test & 0.1842745 & \(<2\times 10^{-16}\) \\ Jarque–[PERSON] Test & 1117.3959565 & \(<2\times 10^{-16}\) \\ D’Agostino Omnibus Test & 182.1690000 & \(<2\times 10^{-16}\) \\ Ljung–Box Test & 124.5937365 & \(<2\times 10^{-16}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Results of normality tests and the correlation test for residuals of neural network.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & \(\mathbf{r}\) & \(\boldsymbol{\sigma_{y}^{pred}}\) \\ \hline Linear regression & 0.958 & 13.987 \\ KNN regression & 0.956 & 13.790 \\ Neural network & 0.956 & 13.717 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Values of correlation between empirical and predicted values of ICRE and standard deviation of predicted ICRE.  
As shown in Table 8 and Figure 10, the validation results for the above models are very similar.  
By examining the standard deviation, correlation coefficient, and RMSE, the Taylor diagram offers a visual overview of the model's performance. The standard deviation of the models shown on the graph is close to \"15\", suggesting that the observed data variability is well matched by the variability in the model predictions. There is a significant linear link between the model predictions and the observed data, as indicated by the correlation coefficient, which reaches roughly \"0.95\". The fact that the models are able to accurately reflect the patterns in the actual data is supported by this result. The concentric grey dashed lines show the RMSE, which is roughly \"5\". This indicates that the models are very accurate and that the prediction errors are reasonably low. There is a high degree of similarity in the performance of the shown model points because they are close together and have different symbols. Nonetheless, depending on some parameters, one model can be marginally more accurate than the other due to minor discrepancies in the point locations. All models show a good fit to the data, according to the Taylor diagram, with high correlation, low RMSE, and comparable variability levels. This proves that the models can produce accurate predictions; picking one over the other can be the result of small variations in performance.  
On the test set, the following forecast accuracy measures were estimated: RMSE, MSE, MAE. The results are presented in the Table 9.