## 3 Results
Notice that in both schools SI concentration negatively correlates with all particle channels (Pearson correlation coefficient is \(-0.36\) for total particle concentration measured by TSI Nanoscan and \(-0.39\) for total particle concentration measured by TSI OPS in School 1, and \(-0.09\) and \(-0.37\) in School 2), and that it positively correlates with radon (Pearson correlation coefficient is 0.33 and 0.59 in Schools 1 and Schools 2 respectively). This coincides with the conclusions that can be made from Equations (3), (4) and (6), and therefore it is justified to use these equations as a starting point for development of statistical models. It is clear looking at TSI Nanoscan and OPS channels in the correlation matrix, that larger groups of channels correlate and thus it wouldn't be useful to consider all channels as independent predictors (signals) in the framework of regression modelling due to multicollinearity effects. We have, therefore, reduced the number of predictors for particulate matter we use in the modelling to the most significant ones. This can be done in a number of ways, and in statistical modelling this technique is known as feature selection [25]. However, at this stage, in order to keep physical interpretation of predictors possible, we have opted not to use principal component analysis and similar methods for feature selection, and aggregated particle channels into larger size bins, approximately corresponding to groups of correlated channels depicted in Figure 3. Aggregations that were used are shown in Table 2. Aggregations only include consecutive channels, and for that reason in School 2, 11.5 nm channel was excluded from Aggr2, despite the high correlation evident from Figure 3. Note that this kind of aggregation somewhat lacks in terms of desirable properties of predictors (such as low cross correlation) that could be achieved via use of principal component analysis (PCA) [25], however, it still preserves \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline  & \multicolumn{2}{c}{**Negative**} & \multicolumn{2}{c}{**Radio**} & \multicolumn{2}{c}{**Particle conc.**} & \multicolumn{2}{c}{**Particle conc.**} & \multicolumn{2}{c}{**Pressure**} & \multicolumn{2}{c}{**t**} & \multicolumn{2}{c}{**RH**} \\  & \multicolumn{2}{c}{**Small Ions**} & \multicolumn{2}{c}{**Radon**} & \multicolumn{2}{c}{**10–420 nm**} & \multicolumn{2}{c}{**0.3–10 um**} & \multicolumn{2}{c}{**(atm)**} & \multicolumn{2}{c}{**[\({}^{\circ}\)C]**} & \multicolumn{2}{c}{**[\%]**} \\  & \multicolumn{2}{c}{**[\#/cm\({}^{3}\)]**} & \multicolumn{2}{c}{**[\#/cm\({}^{3}\)]**} & \multicolumn{2}{c}{**[\#/cm\({}^{3}\)]**} & \multicolumn{2}{c}{**[\#/cm\({}^{3}\)]**} & \multicolumn{2}{c}{**[\#/cm\({}^{3}\)]**} \\ \hline  & S1 & S2 & S1 & S2 & S1 & S2 & S1 & S2 & S1 & S2 & S1 & S2 & S1 & S2 \\ Min & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 776.5 & 53.2 & 30.4 & 0.97 & 0.98 & 19.60 & 20.12 & 18.97 & 18.87 \\ Max & 871.0 & 643.0 & 118.0 & 234.0 & 95,023.6 & 116,127.2 & 541.9 & 572.6 & 1.00 & 1.01 & 28.81 & 32.62 & 46.14 & 49.18 \\ Mean & 239.9 & 104.8 & 36.8 & 56.5 & 2512.7 & 15,198.2 & 161.1 & 151.1 & 0.98 & 1.00 & 24.24 & 26.64 & 29.77 & 31.20 \\ Med. & 212.0 & 63.0 & 39.0 & 41.0 & 1577.5 & 3724.6 & 142.7 & 132.8 & 0.98 & 1.00 & 24.27 & 26.78 & 29.40 & 30.81 \\ Std. dev & 143.8 & 113.9 & 22.2 & 41.6 & 4283.2 & 31,759.4 & 82.3 & 81.3 & 0.01 & 0.01 & 1.80 & 2.00 & 6.23 & 5.37 \\ \hline \end{tabular}
\end{table} 
Table 1: Summary statistics (minimum, maximum, mean, median and standard deviation) of air quality variables for the campaign conducted in Schools 1 (S1) and 2 (S2). possibility for relatively simple interpretation of model parameters in linear regression. Later we will also explore the possible benefits of PCA for aggregation of particle channels in the context of predictive modeling. Figure 2: Radon concentration (dotted) vs. small ion concentration (full line) in (**a**) School 1 and (**b**) School 2.