## 3 Methodology
### Methods of Predictive Modeling
#### 3.4.2 Evaluation of Metrics of Prediction Models
Furthermore, our experiments with transfer learning, where a model trained on Al Riyadh data was further trained on Al Jubail data, did not yield any significant improvement in predictive performance. When we find a positive linear relationship between two pollutants, this may suggest similar sources for these pollutants. We found this positive relation in Al Riyadh between NO2 and CO and between HCHO and O3. The pollution, in this case, may be attributed to the large number of vehicles and the extensive construction activities. In Al Jubail, there is a positive relationship between NO2 and SO2, between NO2 and HCHO, and between HCHO and SO2. The pollution, in this case, may be attributed to the emissions from industrial activities. In Najran, there is a negative relation between O3 and CO. Given that these two pollutants are at their lowest levels in Najran in comparison to Al Riyadh and Al Jubail, based on [50], we can conclude that when CO is present, it can react with O3, forming CO2 and reducing the amount of O3 available. Additionally, CO can absorb sunlight, which is essential for O3 formation. As a result, high levels of CO can limit O3 production in the atmosphere, creating a negative correlation between these two pollutants. After this, data processing and [PERSON]'s ANOVA for air pollutants (NO2, SO2, CO, O3, and HCHO) for the years 2022 and 2023 were carried out across the three cities in the Kingdom of Saudi Arabia, classified as industrial, agricultural, and high population, using the Python3 programming language. [PERSON]'s ANOVA was applied instead of standard ANOVA due to the violation of the assumption of homogeneity of variances among the groups. This method is robust to unequal variances and is considered more appropriate when the assumption of equal variances is not met [54; 55]. [PERSON]'s ANOVA tested the main effects of the independent factors (city and year) and their interaction with each pollutant, adjusting for unequal variances. For each factor, the \(p\)-value was calculated. The null hypothesis was rejected if the \(p\)-value obtained from [PERSON]'s ANOVA was less than the chosen significance level (in our case, alpha = 0.05). Rejection of the null hypothesis indicates statistically significant differences in the average pollution levels between the three cities during the two years. As shown in Table 7, the probability values from [PERSON]'s ANOVA for all the air pollutants show the identification of the interaction effect between the independent factors and the dependent factors. For example, we found that the NO\({}_{2}\) pollutant has a significant main effect on the \"city\" factor (\(p\)-value = 1.583702 \(\times\) 10\({}^{-167}\)) and that there is a relationship between the city characteristics and the concentration rate of the pollutant. This means there are differences in the dependent factors across levels of the independent factor of the city. However, the lack of a significant main effect for the independent \"year\" factor (\(p\)-value = 9.72024 \(\times\) 10\({}^{-1}\)) indicates that levels of this factor are not associated with significant changes in NO\({}_{2}\) levels. As for the dependent factor sulfur dioxide (SO\({}_{2}\)) and its relationship with the \"city\" and \"year\" variables, it was found that the \"city\" factor has a significant effect on the SO\({}_{2}\) concentration, as proven by the low probability value (\(p\)-value = 1.840551 \(\times\) 10\({}^{-45}\)), and this indicates a significant difference in the SO\({}_{2}\) concentration between the cities analyzed. Meanwhile, the \"year\" factor shows no significant effect on the SO\({}_{2}\) concentration and has a high \(p\)-value (\(p\)-value = 1.75437 \(\times\) 10\({}^{-1}\)). In summary, [PERSON]'s ANOVA reveals that the \"city\" factor has a stronger effect, while the \"year\" factor shows a weaker effect on the SO\({}_{2}\) concentration.