Pearson correlation analysis
The Pearson correlation coefficient was determined by constructing a heatmap for the concentration of various pollutants (pre and during pandemic confinement) among populous sites of four metropolitan cities of India, viz. ITO, Delhi, Worli, Mumbai, Jadavpur, Kolkata, and Manali Village, Chennai.

Site 1—ITO, Delhi
At this site, the perfect positive correlation was observed between AQI and PM2.5, a strong positive correlation between AQI-PM10 and PM2.5-PM10, whereas a negative correlation was observed for ozone with AQI and other pollutants. The correlation coefficient between AQI-PM2.5, AQI-PM10, and PM2.5-PM10 was found as 0.98, 0.82, and 0.77 respectively, showing a significantly higher positive relationship. This indicate the changes in PM2.5 and PM10 concentrations have a great influence on AQI content; i.e., an increase in their concentration will directly elevate the air quality index. Besides, AQI-ozone, PM2.5-ozone, and PM10-ozone confirmed low negatively correlated variables, i.e., − 0.31, − 0.38, and − 0.18 respectively indicating the higher values of AQI, PM2.5, and PM10 will lower down the ozone concentration. A feeble correlation exists between AQI-NH3 (0.46), AQI-NO2 (0.38), AQI-SO2 (0.28), and AQI-CO (0.11) showing mild effect on AQI (Fig. 5 (a)).
Fig. 5 Pearson’s correlation heatmap for air pollutants during the pre and COVID-19 pandemic confinement, 2020 among populous sites of four major metropolitan cities in India

Site 2—Worli, Mumbai
Product-moment correlation coefficient analysis for site 2 demonstrates the positive correlation between all of the studied pollutants as shown in Fig. 5 (b). The highest correlations were confirmed between AQI-PM2.5, with a correlation of 0.97, AQI-PM10, with 0.94, and PM2.5-PM10, with 0.91 which demonstrates PM2.5 and PM10 are the most significant dominating factors in elevating the AQI. A correlation value of 0.80, 0.74, 0.72, and 0.86 between AQI-NO2, AQI-NH3, AQI-SO2, and AQI-CO indicates a significant positive relationship, while moderate correlation was determined between CO and ozone concentration (0.53).

Site 3—Jadavpur, Kolkata
A significant positive correlation was observed between the prominent pollutants PM2.5, PM10, NO2, NH3, and CO with AQI, i.e., 0.96, 0.95, 0.86, 0.70, and 0.70 respectively in site 3 as shown in Fig. 5 (c). This implies the studied pollutants had a great impact on air quality among monitoring station of Jadavpur, Kolkata, whereas ozone shows a negative correlation with AQI (− 0.25), and other studied pollutants i.e., PM2.5 (− 0.32), PM10 (− 0.36), NO2 (− 0.48), NH3 (− 0.50), and CO (− 0.35). This indicates mean O3 concentration will significantly increase with a decrease in the mean AQI, PM2.5, PM10, NO2, NH3, and CO concentrations.

Site 4—Manali Village, Chennai
Pearson’s correlation heatmap for Manali Village, Chennai demonstrates significant positive correlations for PM2.5 (0.69) and PM10 (0.73) with AQI, while other pollutants exhibit a moderate or negative correlation. The lowest values of correlation coefficient were found for the pairs AQI-NO2 (0.26), AQI-NH3 (0.04), and AQI-CO (0.33) indicating mild association between these variables; i.e., the effect of concentration of NO2, NH3, and CO on air quality is minimal. However, the approximately zero correlation between AQI-SO2 (0.009) and AQI-ozone (0.01) indicates no linear relationship, but there may be some other strong non-linear relationship between the two variables (Fig. 5 (d)). In other words, we can say that the simple linear function cannot describe its relationship in depth.