# Influence of Particulate Matter and Carbon Dioxide on Students' Emotions in a Smart Classroom
## 3 Results  
This section explores the relationships between environmental factors, including PM\({}_{1}\), PM\({}_{2.5}\), PM\({}_{10}\), and CO\({}_{2}\), and students' emotions (anger, disgust, fear, happiness, sadness, surprise, and neutral). The analysis begins with [PERSON]'s correlations between each environmental factor and emotions are examined. Following this, linear regression models are developed for each emotion. A general summary of the models is provided to facilitate the understanding of key findings. To provide an overview of the relationships between the environmental factors and emotions, a heatmap is presented (Figure 2). This heatmap summarizes the strength and direction of the correlations, using warmer colors to indicate positive correlations and cooler colors for negative correlations. The significance levels are marked (* \(p\) < 0.05, ** \(p\) < 0.01, *** \(p\) < 0.001), highlighting the robustness of these associations. The variables PM\({}_{1}\), PM\({}_{2.5}\), and PM\({}_{10}\) exhibited high and positive correlations among themselves, all with significant Spearman correlation coefficients (\(p\) < 0.001), suggesting a strong relationship between these particles. Additionally, a significant negative correlation is observed between PM\({}_{1}\), PM\({}_{2.5}\), and PM\({}_{10}\) with CO\({}_{2}\) (\(p\) < 0.001), indicating an inverse relationship. Various correlations between emotions and environmental variables were observed in this study. Regarding PM, some significant and weak associations with emotions were found. For instance, PM\({}_{1}\) showed a significant and negative correlation with surprise. PM\({}_{2.5}\) showed a significant and negative correlation with surprise (rho = -0.03, \(p\) < 0.001) and positive with happiness (rho = 0.03, \(p\) < 0.001), while PM10 exhibited correlations with surprise (rho = -0.04, \(p\) < 0.001) and anger (rho = 0.03, \(p\) < 0.001). Furthermore, the concentration of CO\({}_{2}\) showed stronger correlations with various emotions. Positive associations were found between CO\({}_{2}\) and emotions such as anger (rho = 0.098, \(p\) < 0.001) and disgust (rho = 0.078, \(p\) < 0.001), and negative associations with sadness (rho = -0.051, \(p\) < 0.001) and fear (rho = -0.031, \(p\) < 0.001). Building on the correlations observed, we further examined the predictive power of the environmental variables using regression models. Table 3 provides a summary of these models, highlighting the efficacy of CO\({}_{2}\), PM\({}_{1}\), PM\({}_{2.5}\), and PM\({}_{10}\) in predicting basic emotions. This analysis offers insight into how these environmental factors influence emotions, beyond the correlation analysis. The models for neutral, fear, sadness, surprise, and happiness emotions showed substantial R\({}^{2}\) values, ranging from 0.364 for happiness to 0.622 for neutral, indicating that a significant proportion of variance in these emotions is explained by the predictors used in the models. All models, except for anger (R\({}^{2}\) = 0.000), are statistically significant with \(p\)-values less than 0.001, supporting the robustness of the models. The Durbin-Watson statistics for all models are close to 2, suggesting no significant autocorrelation in the residuals, ensuring the reliability of the regression estimates.