## 4 Forecasting Results and Discussion
### Evaluation and Discussions  
As shown in Table 7 and Figure 12, the forecasting accuracy varies depending on the different models used. We can also observe that the LSTM model has the best accuracy as it can capture the daily consumption pattern. The FBP-FBP is the best performing hybrid model, despite the 68% accuracy; this can be explained by the ability of FBP to incorporate seasonality (e.g., holidays) into its forecast, and with FBP as the second model, its accuracy can be optimised by taking into account unusual consumption patterns.  
Figure 11: Testing data vs forecasted data from Multistage Hybrid model, with FBP as first model and LSTM as second model, of the hospital’s electricity demand.  
Figure 10: MAE, \(R^{2}\), and RMSE values for the multistage hybrid models with and without temperature as a feature. (**a**) Mean Absolute Error (MAE). (**b**) Coefficient of Determination (\(R^{2}\)). (**c**) Root Mean Square Error (RMSE).  
To further investigate the success of FBP-FBP, we present the residuals from the first FBP model. From the residual values shown in Figure 13, we can observe that the vast majority of the values lie between \(-10\) and \(10\), except for the outliers, which can have a major effect on the error values. To better evaluate the residuals, we plotted their histogram in Figure 14. We can observe that the residuals can be modeled as a normal distribution  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Model** & & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** \\ \hline \multirow{6}{*}{\begin{tabular}{c} Without \\ Temperature \\ as a Feature \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} Single \\ \end{tabular} } & LASSO & \(-0.76\%\) & 5.05 & 5.83 \\ \cline{3-5}  & & SVR & 44.35\% & 3.17 & 4.34 \\ \cline{3-5}  & & FBP & 68.68\% & 2.51 & 3.25 \\ \cline{3-5}  & & LSTM & 87.20\% & 1.55 & 2.08 \\ \cline{3-5}  & & FBP-SVR & 67.86\% & 2.56 & 3.29 \\ \cline{3-5}  & & FBP-LSTM & 68.22\% & 2.54 & 3.28 \\ \cline{3-5}  & & SVR-LSTM & 42.70\% & 3.32 & 4.40 \\ \cline{3-5}  & & SVR-SVR & 43.57\% & 3.17 & 4.37 \\ \cline{3-5}  & & FBP-FBP & 68.06\% & 2.52 & 3.28 \\ \hline \multirow{6}{*}{\
\begin{tabular}{c} With \\ Temperature \\ as a Feature \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} Single \\ \end{tabular} } & LASSO & 10.15\% & 4.61 & 5.51 \\ \cline{3-5}  & & SVR & 44.99\% & 3.12 & 4.31 \\ \cline{3-5}  & & FBP & 27.61\% & 3.82 & 4.94 \\ \cline{3-5}  & & FBP-SVR & 67.97\% & 2.55 & 3.29 \\ \cline{3-5}  & & FBP-LSTM & 67.13\% & 2.60 & 3.33 \\ \cline{3-5}  & & SVR-LSTM & 39.62\% & 3.35 & 4.52 \\ \cline{3-5}  & & SVR-SVR & 44.14\% & 3.13 & 4.34 \\ \cline{3-5}  & & FBP-FBP & 68.81\% & 2.51 & 3.25 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Forecasting performance results for all models: R\({}^{2}\), MAE, and RMSE values.  
Figure 12: Results of the comparative study showing the MAE, \(R^{2}\), and RMSE values of all models. (**a**) Mean Absolute Error (MAE). (**b**) Coefficient of Determination (\(R^{2}\)). (**c**) Root Mean Square Error (RMSE).  
with a relatively narrow variance. Thus, the second FBP would use the residuals and build an accurate forecast, ultimately optimising the accuracy.