# A Comparative Analysis for Air Quality Estimation from Traffic and Meteorological Data
## 3 Results  
In this section, the results obtained from the aforementioned tasks are presented. The discussion will first focus on regression results, analysing the advantages and drawbacks of the employed techniques over each pollutant and time window, for both Hourly Set and Daily Set, subsequently the AQI prediction estimates will be presented and assessed. As summarized in Table 6, the results on the regression task over the pollutants with hourly resolution is in line with expectations. The performance on the Hourly Set without lagged variables, displayed on the columns marked with \(w=0\), highlights on average better results for simpler models: in every case, the best values in terms of RMSE were achieved by the linear model or the Random Forest regressor, with the only exception of \(NO_{x}\) where the BRNN obtained a slightly smaller error. The second configuration, indicated by \(w=24\), displays results obtained with lagged variables over a 24-h period. In this case, the longer window allowed the models to reach better estimates in most cases, with a relevant edge of RF in half of the considered pollutants. Here the exceptions are represented by the benzene (\(C_{6}H_{6}\)), where the linear model outperformed the other solutions, and the ozone (\(O_{3}\)), where the LSTM surpassed the linear regressor by a small margin. These values might be explained by the higher autocorrelation of these two pollutants on the 24-hour mark, visible in Table 4, together with the strong periodic patterns of the ozone influenced by solar radiation that could favour sequence-based solutions like LSTM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Quality** & **Index** & \(\mathbf{NO_{2}}\) & \(\mathbf{O_{3}}\) & \(\mathbf{PM_{10}}\) \\ \hline Very low & 0–25 & 0–50 & 0–60 & 0–15 \\ Low & 25–50 & 50–100 & 60–120 & 15–30 \\ Medium & 50–75 & 100–200 & 120–180 & 30–50 \\ High & 75–100 & 200–400 & 180–240 & 50–100 \\ Very High & \textgreater{}100 & \textgreater{}400 & \textgreater{}240 & \textgreater{}100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Common Air Quality Index (CAQI) reference table. Indices of individual pollutants correspond to hourly concentrations (\(\mu\)g/m\({}^{3}\)), except for the 24-h index for \(PM_{10}\). The common index is defined as the worst quality among sub-components. Further increasing the time interval, as summarized in the last column (\(w=48\)), does not seem to introduce a relevant advantage over previous solutions, as the error rates computed on the new estimates appear roughly the same. Again, the only exception is represented by the LSTM model, that obtained better results for the majority of pollutants, but most importantly consistently reduced its error with respect to the previous 24-h configuration. Not surprisingly, a deep recurrent neural network can outperform standard machine learning techniques taking advantage of the sequential structure of the data; however, we note that, even in this case, the results are only marginally better than, for instance, the linear regressor. This could be very well caused by the strong limitation on the time interval considered, nevertheless a longer window did not represent a viable comparison because of the feature explosion caused by the introduction of lagged variable in the other configurations. The results over the Daily Set are shown in Table 7. In this case, we carried out the same evaluation procedure, running the models over the test set and computing the error metrics for each pollutant and estimator, in three different time windows corresponding to lags of one and two days, which are comparable with the 24 and 48-h shifts in the Hourly Set. Unfortunately, due to the lack of data and lower resolution of the available signals, the results are far from optimal, when compared to the hourly counterpart. However, the RMSE values presented are consistent with the data distribution, displayed in Table 8, and both linear and Random Forest regressors display good performances in the setups with window size \(w=0\) and \(w=1\).