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Table 1

Summary of all the discussed OLS/WLS relations.

y − x Sample N c 0 c 1 RMS PCC log (pP) ρ log (pS)
c 46 1.15 ± 0.39 − 0.15 ± 0.15 0.08 0.15 − 0.48 0.21 − 0.73
c 46 − 0.47 ± 0.35 − 0.04 ± 0.01 0.07 − 0.46 − 2.66 − 0.46 − 2.67
c 46 − 1.59 ± 0.36 − 0.08 ± 0.01 0.07 − 0.69 − 6.41 +0.67 − 5.95
c 46 − 2.23 ± 0.35 − 0.11 ± 0.01 0.07 − 0.78 − − 0.75 −
Δ(B − V)/Δr − log (Leff) c 46 − 1.47 ± 0.32 0.10 ± 0.03 0.07 0.51 3.59 0.50 − 3.37
log() g 261 2.82 ± 0.02 − 0.99 ± 0.05 0.21 − 0.79 − − 0.75 −
log() c 53 2.75 ± 0.29 − 1.02 ± 0.09 0.31 − 0.84 − − 0.57 − 5.09
log(Leff) − log (reff) g 261 9.48 ± 0.02 1.03 ± 0.05 0.40 0.80 − 0.75 −
log(Leff) − log (reff) c 53 9.34 ± 0.29 0.97 ± 0.10 0.33 0.70 − 0.64 − 5.94
log(ℳeff) − log (reff) g 261 10.10 ± 0.03 0.91 ± 0.06 0.31 0.64 − 0.59 −
log(ℳeff) − log (reff) c 20 10.10 ± 0.03 0.91 ± 0.06 0.26 0.54 − 1.94 0.40 − 1.16
log(Leff) − log (σ) g 261 6.09 ± 0.21 1.73 ± 0.10 0.23 0.75 − 0.78 −
log(Leff) − log (σ) c 41 7.90 ± 1.59 1.63 ± 0.56 0.39 0.42 − 2.25 0.38 − 1.88
log(reff) − log (σ) c 41 1.93 ± 0.33 1.56 ± 0.68 0.47 0.34 − 0.35 −
log(reff) − log (n) g 261 − 0.28 ± 0.04 1.33 ± 0.08 0.26 0.49 − 0.49 −
log(reff) − log (n) c 38 2.97 ± 0.07 1.02 ± 0.12 0.24 0.33 − 1.35 0.40 − 1.91
log(Leff) − log (n) g 261 9.09 ± 0.05 1.58 ± 0.09 0.32 0.44 − 0.47 −
log(Leff) − log (n) c 38 12.08 ± 0.09 1.08 ± 0.22 0.48 0.05 − 0.12 − 0.12 − 0.31
log(σ) − log (Lsub/Lmain) c 22 2.92 ± 0.03 0.12 ± 0.06 0.08 0.43 − 1.36 0.49 − 1.68

Notes. y- and x-axis (Col. 1), sample used to compute the relation (Col. 2, where g = galaxies and c = clusters), sample size (Col. 3), zero-order polynomial term (Col. 4), first-order polynomial term (Col. 5), RMS (Col. 6), Pearson correlation coefficient PCC (Col. 7), Pearson p-value in logarithmic units (Col. 8, where the unreported values indicate a probability smaller than 3 × 10-7, which comes from the 5 RMS criterion), Spearman’s rank correlation ρ (Col. 9), Spearman p-value in logarithmic units (Col. 10, where the unreported values again indicate a probability smaller than 3 × 10-7).

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