# Multivariate Regression Modeling for Coastal Urban Air Quality Estimates
## 3 Results
### Validation of Multivariate Models  
Figure 9 shows that the temporal distribution of the measured (observed) and calculated values for PM\({}_{10}\), PM\({}_{2.5}\), NO\({}_{2}\), SO\({}_{2}\), O\({}_{3}\) and CO denoted the behavior throughout each period, such as before, during and after the yellow sand periods. These figures display the real-time hourly forecasting values for PM\({}_{10}\)_K(N), PM\({}_{2.5}\)_K(N), NO\({}_{2}\)_K(N), SO\({}_{2}\)_K(N),  
Figure 8: As Figure 6, but for after the event from 23 March to 27 March 2015. PM\({}_{10}\) (a), PM\({}_{2.5}\) (b) (\(\upmu\)g/m\({}^{3}\)) and NO\({}_{2}\) (\(\times\)1000) (c), SO\({}_{2}\) (\(\times\)1000) (d), O\({}_{3}\) (\(\times\)1000) (e), and CO (\(\times\)100) (f) ppm. O3-K(N) and CO-K(N) calculated by multivariate regression models with the three-hours-earlier data before, during and after the yellow sand periods. Through the comparison of the predicted and measured values, we investigated in which time period the applicability of the predicted values to the measured ones was better. Before the yellow sand period, the difference in the applicability of the real-time predicted values to the measured ones could be shown by the Pearson regression coefficients  
Figure 9: Temporal variations of the measured and real-time predicted values of PM\({}_{10}\) (**a**), PM\({}_{2.5}\) (**b**) (\(\mu\) g/m\({}^{3}\)) and NO\({}_{2}\) (\(\times\)1000) (**c**), SO\({}_{2}\) (\(\times\)1000) (**d**), O\({}_{3}\) (\(\times\)1000) (**e**) and CO (\(\times\)100) (**f**) (ppm) in Kangnung Korea. of PM\({}_{10}\)_K(N) (0.957), PM\({}_{2.5}\)_K(N) (0.906), NO\({}_{2}\)_K(N) (0.886), O\({}_{3}\)_K(N) (0.932) and CO\({}_{K}\)(N) (0.864), which were slightly higher than for SO\({}_{2}\)_K(N) (0.795). Therefore, the real-time predicted values of PM\({}_{10}\)_K(N), PM\({}_{2.5}\)_K(N), NO\({}_{2}\)_K(N), SO\({}_{2}\)_K(N), O\({}_{3}\)_K(N) and CO\({}_{K}\)(N) fit their measured values very well; even the predicted values of SO\({}_{2}\)_K(N) were only slightly more deviated from the measured ones. During the yellow sand event, all of the real-time predicted values fitted the measured values much better than before the event, except for NO\({}_{2}\)_K(N), which had a slightly lower correlation coefficient. After the event, the real-time predicted values still fitted with the measured values very well and were similar to the cases before and during the yellow sand period. As a result, the real-time predicted values of PM\({}_{10}\)_K(N), PM\({}_{2.5}\)_K(N), NO\({}_{2}\)_K(N), SO\({}_{2}\)_K(N), O\({}_{3}\)_K(N) and CO\({}_{K}\)(N) were all very close to their measured values, showing that they were reproduced well, even though the applicability of SO\({}_{2}\)_K(N) was slightly more deviated before the yellow sand event. This means that there is a time gap between their concentrations or it has a slightly bigger or smaller value in the higher and the maximum concentrations before the period. This may be attributed to a slightly lower correlation coefficient, as shown in Figure 6 and Table 2.  
We further compared our simulation results using multivariate regression models and artificial neural network models with similar scientific works by several scientists in Table 8. As hourly averaged or daily averaged pollutant concentrations with or without meteorological data were used differently by individual scientists, it is not easy to compare the results calculated by each other. However, even though the same kinds of input data for the model were used, it is desirable to compare the accuracy of the different model performances. Thus, the comparison results in Table 8 show that the correlation coefficients between the hourly predicted and measured values calculated by our multivariate regression models were 0.886 to 0.982. The accuracy of our calculated values is in the middle range compared with the results calculated using various models by other authors.