## 3 Methodology
### Methods of Descriptive Analysis  
To apply the descriptive analysis, we implemented many statistical methods. A summary of the aggregated data is provided in Table 2, which presents the mean and standard deviation of the air pollutants of all three cities during the years 2022 and 2023.  
Moreover, to investigate the correlation among these pollutants, we used the Pearson correlation coefficient, which measures the linear correlation between two datasets. Its value usually ranges from \(-1\) (high negative correlation) to \(1\) (high positive correlation). A value closer to zero indicates a weaker or non-existent linear relationship. By calculating the Pearson correlation coefficient, we aimed to determine whether these pollutants have a positive or negative relationship, indicating whether they increase or decrease together. In addition, we calculated the correlations between the pollutant NO\({}_{2}\) and meteorological features, such as temperature and humidity, to conduct further analysis on this pollutant. We had two reasons for selecting this pollutant specifically. First, we noted in our results that all the pollutants had the highest concentration in the industrial city except for NO\({}_{2}\), and hence, we investigated its correlation with the weather data. Second, we noticed that all the pollutants were affected by the increase and decrease in weather parameters, and so concluded that it was sufficient to present only one of these pollutants.  
In addition to studying the correlation between air pollutants, we also used the heat map method to visualize spatial variations in pollutant concentrations and meteorological characteristics during all months during the years 2022 and 2023.  
To evaluate the effects of the city and the year on the air pollutant levels, one critical method of the analysis involved using a two-way analysis of variance (ANOVA). Two-way ANOVA is a powerful statistical technique that simultaneously examines two independent variables and their interaction with a dependent variable. In this study, the independent variables were the city and the year, while the dependent variables were the five air pollutants. By applying two-way ANOVA, we examine whether the city or the year had a significant impact on the air pollution levels and whether there was a correlation between the two factors. This analysis provided valuable insights into the relative contributions of city-specific characteristics and temporal trends to air quality variations.  
The two-way ANOVA variables are described based on these three parameters:  
* City, which denotes the characteristics of the city, which include industrial, agricultural, and population density.
* Year, which means the year of reading the data from a city during 2022 and 2023.
* Air pollutants, which denote the concentration of pollutants in each city in a specific year.  
Additionally, the null and alternative hypotheses were determined as follows: There is no significant difference in the mean pollution levels among the three cities, which is the null hypothesis (H0). The alternative hypothesis (H1) depends on whether there is a significant difference in the mean of the pollution levels among the three cities.