Correlation plots ordered by their slope, β. Dark purple colours show HCN, purple HCO⁺ and pink HNC. Top row: integrated intensities of the dense gas tracers (ordered by their slope, β) versus Σ_SFR. Middle row: integrated intensity of CO(2−1) – an indicator of the mean volume density – versus the line ratio with CO(2−1) – a spectroscopic tracers of f_dense. Bottom row: integrated intensity of CO(2−1) – an indicator of the mean volume density – versus the ratio of Σ_SFR with the dense gas tracers – a spectroscopic tracers of SFE_dense. The linmix fits (accounting for upper limits) are shown as solid lines surrounded by 3σ confidence intervals (shaded regions of corresponding colours). Absolute uncertainties are plotted on each data point, which are generally small towards the regions NUC, NBE and SBE. We find the highest uncertainties in the outskirts in our Σ_SFR map. Correlations including HNC result in 58 significant sight lines and 15 upper limits (denoted as light pink markers). We display in each panel Pearson’s correlation coefficient and the power-law slope, intercept and p-value (see Table 6).