The phrase "regression line" refers to a line that represents the general trend or pattern of a set of data points. It helps to predict or estimate the values of the dependent variable based on the values of the independent variable. Full definition
To illustrate this interaction, the Figure 1 shows separate estimated regression lines for these 2 treatment groups for maltreatment involving the study child. (jamanetwork.com)
In particular, I'm interested because you talk about confidence intervals round regression lines. (wmbriggs.com)
A least - squares fit regression line for the simulations (solid line) and the observed seasonal cycle Δαs / ΔTs value based on ISCCP and ERA40 reanalysis (dashed vertical line) are also shown. (ipcc.ch)