Line-strength ratio of the H₂O J_Ka,Kc = 2_1,2−1_0,1 transition and CO J = 15−14 transition as a function of the mass-loss rate Ṁ_g. The data points are color coded according to the variability type: Miras in red, SR/Mira sources in blue, the SRa source in green, and SRb sources in black. A black cross superimposed on a point indicates that the H₂O line strength is flagged as a blend (see Sect. 2.3 for clarification). The gray lines show the individual Monte Carlo linear fitting results to the data points for Miras and SRa sources. The green arrow indicates the mean linear relation (see Sect. 3.3).