# Attention Horizon as a Predictor for the Fuel Consumption Rate of Drivers
## 2 Materials and Methods
### Extraction of Red Light-Approaching Trajectories
An interesting path for future work can be investigating the effect of different environmental factors on the AH values. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Time Periods for AH and FCR Calculation**} \\ \cline{2-4}  & **Calendar Days** & **Calendar Weeks** & **Calendar Months** \\ \hline Mean Correlation & 0.057 & \(-0.200\) & \(-0.213\) \\ Median Correlation & 0.047 & \(-0.156\) & \(-0.402\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean and median of correlations between AH and FCR through time for different drivers when AH and FCR are calculated for calendar days, calendar weeks, and calendar months. Figure 5: Histogram of correlations between fuel consumption rate (FCR) percentile and attention horizon (AH) percentile through time for individual drivers; these parameters are obtained for days (leftmost), weeks (middle), and months (rightmost plot). As we have shown before, the correlation between AH and FCR turns out to be mostly negative for drivers across weeks or months. In other words, a large AH seems to be a predictor of a small FCR within these periods. We suggest that a large AH is a quantitative way of measuring how careful or aware the driver is just before stopping at a traffic light. In this way, AH can be regarded as a metric of general driving efficiency. We found a relationship between AH and FCR, but we would like to propose that AH might also have correlations with other aspects of driving quality. For example, this could include the impact of the driving style on the vehicle's components wear rate or the frequency of traffic accidents for the driver. This is a very interesting aspect for future research on related driving quality metrics other than FCR. We have also established that for bigger periods of time (months and weeks rather than days), there are stronger correlations between AH and FCR. We suspect that this happens due to the impact of uncontrolled variables that change in shorter timescales, i.e., noise; as we increase the timescales, the impact of those variables is reduced under the law of large numbers. In this paper, we discovered that we should normalize AH by traffic light and FCR by vehicle. However, there might be other variables that also need to be controlled for in order to improve the AH or FCR calculations. This is another direction of future work for obtaining more precise values for these parameters. It should also be noted that although for larger time periods the AH-FCR correlation becomes more strongly negative for most of the samples, there are still drivers with positive correlation values. This is an indication that for these drivers, there are still factors whose impact is not smoothed out even when estimating the FCR or AH for timescales of a week or a month. Identifying these factors is another category of future work; in particular, there appear to be some systematic bias factors that are important to understand. This is closely related, but inherently different, from understanding the unknown factors that actually do smooth out during a week or month. A different avenue for research could be the study of variance in AH value during time. Two drivers could have the same average AH in a period of time but one of them can have much more variance. This could potentially lead to higher fuel consumption for one of them compared to the other one. Considering the variance of AH is another potentially interesting subject to focus on for future work. Another research direction is investigating the impact of even longer time periods in the AH metric. In this study, we had access to data with anonymized driver IDs for only three months. However, it could be very interesting to know what we could discover if we had data over the period of several years, allowing us to understand how the driving style evolves in the longer time perspective, based on experience. The scale of the research could be increased in other dimensions, too.