# Influence of Particulate Matter and Carbon Dioxide on Students' Emotions in a Smart Classroom
## 3 Results
For example, for happiness, the linear coefficient is negative (\(\beta\) = \(-0.954\), \(p\)! 0.001) and the quadratic coefficient is  
Figure 3: Explained variance (R\({}^{2}\)) and predictive accuracy (RMSE) for emotions based on environmental factors. ** Statistically significant at \(p\)! 0.001.  
positive (\(\beta\) = 0.552, \(p\) < 0.001). Similarly, for surprise, the linear coefficient is \(\beta\) = \(-\)0.705 (\(p\) < 0.001) and the quadratic coefficient is \(\beta\) = 0.496 (\(p\) < 0.001). For sadness, the pattern was opposite, with a positive coefficient on the linear term (\(\beta\) = 0.961, \(p\) < 0.001) and negative on the quadratic term (\(\beta\) = \(-\)0.636, \(p\) < 0.001), indicating that sadness increases with initial increases in PM\({}_{1}\), but decreases at higher levels of exposure. The analyses for PM\({}_{2.5}\) and its quadratic term (sq_PM\({}_{2.5}\)) show significant effects on several emotions. With fear (\(\beta\) = 0.455, \(p\) < 0.001) and happiness (\(\beta\) = 1.102, \(p\) < 0.001), positive coefficients were observed in the linear term, indicating that higher levels of PM\({}_{2.5}\) are associated with an increase in these emotions. However, the quadratic term showed significant negative effects on both emotions (fear: \(\beta\) = \(-\)0.473, \(p\) < 0.001; happiness: \(\beta\) = \(-\)0.750, \(p\) < 0.001), suggesting a nonlinear inverted U-shaped relationship. For sadness, a significant negative coefficient was found in the linear term (\(\beta\) = \(-\)0.620, \(p\) < 0.001), with a positive quadratic coefficient (\(\beta\) = 0.298, \(p\) < 0.001), indicating a U-shaped behavior, where sadness decreases with initial increases in PM\({}_{2.5}\), but increases at higher levels of exposure. Similarly, surprise showed U-shaped behavior, with a positive coefficient on the linear term (\(\beta\) = 0.483, \(p\) < 0.001) and a negative quadratic coefficient (\(\beta\) = \(-\)0.256, \(p\) = 0.003). Finally, neutral presented a positive quadratic coefficient (\(\beta\) = 0.421, \(p\) < 0.001), suggesting a nonlinear relationship, although no significant effects were found in the linear term (\(p\) = 0.206). The analysis of the effects of PM\({}_{10}\) and its quadratic term (sq_PM\({}_{10}\)) on emotions showed some significant results on surprise and neutral emotions. For the linear term of PM\({}_{10}\), a significant positive coefficient was observed in surprise (\(\beta\) = 0.337, \(p\) < 0.001) and neutral (\(\beta\) = 0.858, \(p\) < 0.001), suggesting that higher levels of PM\({}_{10}\) are associated with an increase in these emotions. The quadratic term (sq_PM\({}_{10}\)) also showed significant effects in surprise (\(\beta\) = \(-\)0.374, \(p\) < 0.001) and neutral (\(\beta\) = \(-\)1.364, \(p\) < 0.001), indicating a nonlinear relationship, with a decrease in these emotions at higher PM\({}_{10}\) levels. For disgust, fear, sadness, surprise, and neutral, CO\({}_{2}\) has a positive and significant impact. Specifically, in disgust (\(\beta\) = 0.048, \(p\) < 0.001), fear (\(\beta\) = 0.115, \(p\) < 0.001), sadness (\(\beta\) = 0.152, \(p\) < 0.001), surprise (\(\beta\) = 0.075, \(p\) < 0.001), and neutral (\(\beta\) = 0.029, \(p\) < 0.001), an increase in CO\({}_{2}\) levels is associated with an increase in these emotions. No significant effects were found in happiness (\(p\) = 0.180). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Predictor** & **Disgust** & **Fear** & **Happiness** & **Sadness** & **Surprise** & **Neutral** \\ \hline PM\({}_{1}\) & \(-\)0.166 & \(-\)0.195 & \(-\)0.954 & 0.961 & \(-\)0.705 & \(-\)0.220 \\  & (0.033) & (0.013) & (\(<\)0.001) & (\(<\)0.001) & (\(<\)0.001) & (\(<\)0.001) & (0.004) \\ \hline PM\({}_{2.5}\) & \(-\)0.075 To better visualize the effects of each environmental variable on emotions, Figure 4 presents the standardized regression coefficients.