## 3 Results
### Results of the Supervised Method
#### 3.2.2 Data Analysis and Results  
In this section, the results of the supervised method for occupancy rate prediction for the test period (15 th to 31 st of August 2017) are presented. The last half of the month August was selected for testing as it was at the end of the available dataset, while the earlier period was used for model training. Weeks before the testing period was usually a period when employees took their summer vacation (from July to early August). Using the vacation weeks as a testing dataset for a model trained on more regular working periods would not give representative results. Another possibility was to shuffle the dataset and use other earlier periods, but using future data to predict history is questionable when dealing with time-series data [38]. However, data sufficiency and generalization analysis in Section 3.2.3. explore different training dataset lengths and testing periods. Each set of predictors with the previously mentioned selected features is presented in Table 3 with error indices. Results show that All predictors have the best result, when looking at the RMSE and explained variation, with slight underprediction, which is shown with a negative MBE value. Light and equipment are showing the second-best results, but with higher underprediction. Total floor \begin{table}
\begin{tabular}{c c c} \hline \hline
**\#** & **Feature** & **Description** \\ \hline
1 & First-order difference (FD) & FD = x\({}_{\text{t}}\) - x\({}_{\text{t}-1}\) \\
2 & Second-order difference (SD) & SD = FD\({}_{\text{t}}\) - FD\({}_{\text{t}-1}\) \\
3 & 1-step Moving average (MA1) & MA\({}_{1}\) = \(\frac{\sum_{i}\times\text{x}_{i+1}}{2}\) \\
4 & 2-step Moving average (MA2) & MA\({}_{2}\) = \(\frac{\sum_{i}+\text{x}_{i+1}}{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of features used in this study and their equation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Main Predictor** & **Selected Features** \\ \hline Lighting & FD\({}_{\text{L}}\), month, hour, weekday \\ Equipment & FD\({}_{\text{L}}\), MA\({}_{2}\), hour, weekday \\ Light and Equipment (separate) & SD\({}_{\text{L}}\), SD\({}_{\text{L}}\), MA\({}_{2}\), MoMe\({}_{2}\), hour, weekday \\ Total floor electric consumption (Light and Equipment summed) & FD\({}_{\text{T}}\), SD\({}_{\text{T}}\), month, hour, weekday \\ Water consumption & FD\({}_{\text{W}}\), MA\({}_{\text{W}}\), MA\({}_{\text{W}}\), hour, weekday \\ All predictors & FD\({}_{\text{L}}\), SD\({}_{\text{L}}\), FD\({}_{\text{L}}\), SD\({}_{\text{L}}\), SD\({}_{\text{W}}\), MA\({}_{\text{L}}\), MA\({}_{\text{W}}\), month, hour, weekday \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected combinations of the features that were used together with the main predictor. electricity consumption shows the lowest absolute MBE value, while the value being positive means that the model using this predictor usually overpredicts. Surprisingly, Water consumption was shown to be a better predictor than Lighting consumption, which was shown as the worst. This confirmed the predictor ranking seen from the correlation matrix (Figure 4). Regarding the explained variation, all results were above 90%, which meant that the models had a good prediction capability where even the model with the Lighting consumption predictor, still showed an average explained variation of 93%. Comparison between ground truth occupancy and predicted occupancy using the best performing model (all predictors) is shown in Figure 5 for the test period. It is possible to see that predicted occupancy was following quite well with the ground truth occupancy and that the most considerable difference between the predicted and ground truth mostly happened during peak hours. During peak hours usually, there was a number of external visitors participating in meetings, which were less likely to consume additional energy for equipment or lighting.