Y_SZ − T relation for the ESZ sample with the best-fit results from a linear fit in the logarithmic space. The fit on the observed data is performed using LIRA (black dotted line). The predictions from the semi-analytic model overlap (magenta dashed line: D14 model; blue dashed line: B13 model). The dot-dashed orange line is obtained from the propagation of the scaling in the E15 formalism (see Eq. (13)).