Upper panel: fitting results for Amati relation with GRB samples in different redshift range (the black line is for the whole sample, the blue line is for 0.125 < z ≤ 1, the green line is for 1 < z ≤ 2, the purple line is for 2 < z ≤ 3, and the red line is for z ≥ 3), where the GRB distance moduli were calibrated by the quasar data. Lower panel: 1D marginalized distributions and 2D plots with 1σ and 2σ contours for luminosity correlation parameters.