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Table 5

Summary of results of the different correlations analyses.

Correlation1 Subsample2 N 3 Least square algorithm4 Outlier rejection algorithm4 Spearman parameters
a b a b ρ 5 g6
Ṁ vs. M Hα 277 1.57 ± 0.23 –7.60 ± 0.15 3.19 ± 0.21 –7.09 ± 0.16 0.38 Weak
Ṁ vs. M U-excess 154 1.94 ± 0.23 –7.93 ± 0.12 3.29 ± 0.25 –7.37 ± 0.15 0.55 Moderate
LX vs. M Hα 277 1.90 ± 0.17 30.33 ± 0.12 2.72 ± 0.17 30.89 ± 0.09 0.52 Moderate
LX vs. M U-excess 154 1.72 ± 0.17 30.59 ± 0.10 1.75 ± 0.12 30.89 ± 0.07 0.61 Strong
Residual LX determined using minimum-square fit analysis7
LX/ LX(Ṁ) vs. Ṁ Hα 277 –0.94 ± 0.05 –8.07 ± 0.40 –1.09 ± 0.04 –9.65 ± 0.39 –0.78 Strong
LX/ LX(Ṁ) vs. Ṁ U-excess 154 –0.53 ± 0.05 –4.72 ± 0.43 –0.67 ± 0.06 –5.85 ± 0.53 –0.63 Strong
Residual LX determined using MCMC outlier rejection fit analysis7
LX/ LX(Ṁ) vs. Ṁ Hα 277 –0.59 ± 0.05 –5.50 ± 0.43 –0.68 ± 0.13 –6.51 ± 1.22 –0.55 Moderate
LX/ LX(Ṁ) vs. Ṁ U-excess 154 –0.19 ± 0.05 –2.04 ± 0.47 –0.35 ± 0.07 –3.28 ± 0.58 –0.29 Weak

Notes. The relations correspond to the logarithmic equation of the parameters.

(1)

Parameters to analyze.

(2)

Subsample from which the data are referred.

(3)

Number of objects in the subsample.

(4)

a stands for the slope of the linear regression and b for the intercept. Errors for the least square analyses are the standard deviation as given in the ODR algorithm. Errors for the outlier analyses are the standard deviation of all the values computed in the MCMC algorithm for each parameter.

(5)

Spearman’s ρ rank correlation coefficient.

(6)

Goodness-of-fit as given by ρ.

(7)

Different regression methods between M∗, LX and Ṁacc yield different LX(Ṁ) equations. Rows five and six show the regression results between LX/LX(Ṁ) and Ṁacc when the OLS method was used for the first regressions, while rows seven and eight, when the outlier rejection methodology was applied.

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