## 4 Results
### Regression Model Analysis  
For the regression model, a least square regression model was applied with the support of the software Eviews 12. The analysis is focused on the dynamics of passengers on the platform of the Francia metro station. The structure of the model (Equation (1)) is based on the following dependent and independent variables, which are described in Table 1:  
* Speed: dependent;
* Dispersion: independent;
* Type of passenger: independent;
* Platform features: independent;
* Detected passengers: independent. \[\text{Speed}=\beta 0+\beta 1\cdot\text{Dispersion}+\beta 2\cdot\text{Type of Passenger}+\beta 3\cdot\text{Platform Features}+\beta 4\cdot\text{Detected Passengers}+\epsilon \tag{1}\]  
where \(\beta 0\) is the constant. \(\beta 1\), \(\beta 2\), \(\beta 3\), and \(\beta 4\) are the coefficients representing the impact of each independent variable on speed, and \(\epsilon\) is the error term. The development of the model is based on the idea that speed is an important variable within the level of service context. Therefore, this model is applied with the objective of understanding the effect of passengers' behaviour and characteristics, in addition to platform features, on the speed of passengers. Table 2 shows the results of the regression model. It is possible to observe that during the first period (7:00-7:20), platform features negatively affect the speed of passengers, while type of passengers, detected passengers, and dispersion positively affect the speed of passengers. In the second period (7:20-7:40), platform features, detected passengers, and dispersion presented a positive effect on speed, while the type of passenger had a negative effect. The third period (7:40-8:00) presented a pattern of the effect of variables on speed similar to the first period, with the exception of dispersion, which presented a negative effect on speed. In general, there is one variable, detected passengers, that maintains a similar effect pattern on the speed of passengers in all periods. The variable of detected passengers indicates that there may be some effect of crowded conditions in the station on speed, meaning that the platform design could be inducing the passengers, even in crowded situations, to exit or enter the platform or the train in an organised manner. The variable platform features show a negative effect on speed in most cases. Regarding the type of passengers, it indicates that, possibly, adults tend to have a higher speed. Concerning the dispersion, as expected, if passengers are more distant from one another, the speed of passengers increases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dimension** & **Variable** & **Description** \\ \hline \hline \multirow{3}{*}{1. Passenger behaviour} & Detected passengers & Number of passengers detected \\  & Speed & Component in x-axis and y-axis, which then is obtained by \\  & & the absolute value (i.e., not the vector) (m/s) \\  & Dispersion & Standard deviation of the average distance between \\  & & passengers (m) \\
2. Train design & Seats, corridors, and central halls & Number, type, and dimensions \\
3. Passenger characteristics & Type of passenger & e.g., children or adults \\  & Height & Height per passenger in each detection (m) \\
4. Train operation & Moment of the day & e.g., peak hour \\  & Train arrival & e.g., presence of the train at the platform \\
5. Platform built environment & Platform location & e.g., inbound or outbound \\  & Platform features & e.g., benches and bins \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of variables in the proposed multidimensional level of service. It is important to highlight that the Francia metro station's operational context presents external factors that may also have an impact on the speed of passengers that were not considered in this analysis and may be affecting the results.