## 4 Experimental Results and Analysis
### Error Analysis with Scatter Plots and Box Plots  
Figure 10 shows the predicted values and true values of the three models, LightGBM, Prophet, and SARIMA, in the form of scatter plots. With the help of the identity function (y = x) image, the gap between the predicted value and the true value can be more intuitively displayed, and it is also convenient to observe the performance of different models in different numerical ranges. The LightGBM model is presented as green scatter points. In months such as May and July, the green scatter points are relatively close to the identity function (y = x) line, which indicates that the model can better capture the distribution trend of PM\({}_{2.5}\) concentration in these months. From the distribution of scatter points, the degree of dispersion is low, indicating that the model prediction results are more stable. However, overall, there is a large deviation between the predicted values of the LightGBM model and the true value range. This may be due to the fact that the LightGBM model allocates weights to data features or fits complex relationships during training, which leads to a certain deviation in capturing the overall range of data. Although it can stably reflect trends, there is still room for improvement in accuracy. In contrast, the blue scatter points of the Prophet model are more loosely distributed, and most of the scatter points deviate downward from the identity function. Taking June and July as examples, the model's predicted values deviate greatly from the true values, indicating that it is insufficient in grasping the trend of PM\({}_{2.5}\) concentration changes in these two months, and the prediction error is large. The Prophet model is mainly based on the seasonality, trend and holiday effects of time series for modeling. If in a specific month, the actual concentration change is affected by some factors that are not fully considered by the model, such as sudden meteorological changes or special human activities, it is easy to cause the model's prediction deviation to increase. The red scattered points of the SARIMA model are the most scattered compared to the other two models. In months such as March and November, the red scattered points are obviously far away from the identity function, showing that the model has a weak ability to capture the trend of PM\({}_{2.5}\) concentration changes in these months. However, it is worth noting that the predicted value range of the SARIMA model is close to the true value range, and there are more scattered points close to the identity function. This is because the SARIMA model, as a classic time series model, can reflect the overall characteristicsof the data to a certain extent when processing time series data with a certain degree of stationarity. However, due to its high requirements for data stationarity, when the data is affected by some sudden or abnormal factors, inaccurate trend capture will occur. Figure 11 presents data in box plots. These plots vividly showcase the distribution characteristics of prediction errors, making it easier to conduct statistical analysis of error conditions. When we analyze, on a monthly basis, the prediction-error distributions of each model, comparing these box plots with the ones of the original data can more intuitively and clearly highlight the unique advantages each model has in predicting PM\({}_{2.5}\) concentrations. The LightGBM model performed well in some months from May to July. From the box plot, the boxes of the predicted data in these months are shorter, indicating that the data has a smaller degree of dispersion, that is, the prediction error is relatively concentrated. At the same time, the median is close to the median of the original data, and the deviation is within 8 \(\mathrm{\SIUnitSymbolMicro m}\)3, which shows that the model can accurately grasp the central trend of the data in these months, and the prediction accuracy and stability are high.