Analysis of a set of synthetic observations that follow an intrinsic β(T) ∝T^B relation. The parameters B and k (noise) of the input simulation are given in the frames and are indicated by solid vertical and horizontal lines. The horizontal dot-dashed and dashed lines correspond to the values of B and the β rms dispersion, respectively, which are estimated from one realisation of synthetic observations. The other curves show B (dot-dashedred line) and the rms dispersion (blue dashed line) from simulations as a function of the noise scaling k (noise).