Ratio of observed to calculated (3, 3) main beam brightness temperatures compared to the ratio of the (3, 3) to (1, 1) linewidths as a contour plot in the top panel and as a scatter plot in the middle panel. The correlation plot of the rotational temperature and observed to calculated (3, 3) main beam brightness temperature ratio is displayed in the lowest panel. Red points show sources that are not detected in the NH₃ (3, 3) line. Green dashed curves indicate very low hot core beam filling factors between 0.008% and 0.15%.