Table 2.

Scaling relations and intrinsic scatter data from the multi-response regression, as described in Sect. 3.

Description Relation Parameter Results S − S
Intercept Mgas, 300 kpc − Mgas, 300 kpc [0]
Intercept T300 kpc − Mgas, 300 kpc 1.60 ± 0.17
intercept 2.39 ± 0.13
Slope Mgas, 300 kpc − Mgas, 300 kpc [1] 1
Slope T300 kpc − Mgas, 300 kpc 0.71 ± 0.09 1
Slope 1.94 ± 0.07 2
Time evolution Mgas, 300 kpc − Mgas, 300 kpc [0] 0
Time evolution T300kpc − Mgas, 300 kpc 0.68 ± 0.09 0
Time evolution 0.15 ± 0.55 0
Intrinsic scatter Mgas, 300 kpc|Z 0.03 ± 0.01
Intrinsic scatter T300 kpc|Z σt(Y)|Z 0.09 ± 0.02
Intrinsic scatter σl(Y)|Z 0.05 ± 0.03
Scatter correlation T300 kpc − Mgas, 300 kpc|Z 0.35 ± 0.52
Scatter correlation 0.40 ± 0.43
Scatter correlation ρt(Y)l(Y)|Z 0.07 ± 0.70

Notes. The gas mass mg, the temperature t, and the luminosity l act as y1, y2, and y3, respectively. Y1 is an unbiased but scattered proxy of Z. Scatter data and correlations are meant as weighted averages over the redshift range. Values in square brackets are kept fixed in the regression. The last column lists the self-similar expectations. Quoted values are biweight estimators of the marginalised distributions.

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