Table 3.
Correlation parameters between z, log(Lbol), and alternative CF proxies also considering alternative datasets.
| Subset | Parameters | ρR x ∣ y (p-value) | τR x ∣ y (p-value) | ⟨a0⟩ | ⟨a1⟩ |
|---|---|---|---|---|---|
| (1) | (2) | (3) | (4) | (5) | (6) |
| R2−5 μm | z − R | 0.457 (4 × 10−4) | 0.121 (0.135) | 0.247 ± 0.004 | 0.008 ± 0.006 |
| R2−5 μm | log(Lbol)−R | −0.760 (2 × 10−11) | −0.495 (< 104) | 0.250 ± 0.001 | −0.034 ± 0.008 |
| Rpeak − 1μm | z − R | −0.024 (0.863) | −0.105 (0.196) | 0.426 ± 0.013 | 0.001 ± 0.016 |
| Rpeak − 1μm | log(Lbol)−R | −0.454 (5 × 10−4) | −0.323 (104) | 0.424 ± 0.008 | −0.076 ± 0.017 |
| RS16 | z − R | 0.057 (0.678) | −0.099 (0.216) | 0.494 ± 0.005 | −0.004 ± 0.004 |
| RS16 | log(Lbol)−R | −0.770 (6 × 10−12) | −0.563 (< 104) | 0.497 ± 0.002 | −0.030 ± 0.007 |
| CFL13 | z − R | 0.057 (0.678) | −0.099 (0.221) | 0.279 ± 0.004 | −0.004 ± 0.004 |
| CFL13 | log(Lbol)−R | −0.770 (6 × 10−12) | −0.563 (< 104) | 0.282 ± 0.002 | −0.028 ± 0.006 |
| no-corr | z − R | 0.148 (0.280) | −0.044 (0.588) | 0.331 ± 0.006 | −0.000 ± 0.007 |
| no-corr | log(Lbol)−R | −0.745 (7 × 10−11) | −0.536 (< 104) | 0.335 ± 0.003 | −0.046 ± 0.012 |
| no-col | z − R | −0.011 (0.936) | −0.146 (0.073) | 0.371 ± 0.008 | −0.009 ± 0.010 |
| no-col | log(Lbol)−R | −0.718 (7 × 10−10) | −0.522 (< 104) | 0.375 ± 0.004 | −0.059 ± 0.014 |
Notes. Columns represent respectively: alternative CF proxy or alternative dataset (1) described in the text; correlated/fitted parameters (2); Spearman partial correlation index between CF and parameter x keeping y fixed and relative p-value (3); Kendall τ partial correlation index between CF and parameter x keeping y fixed, and relative p-value (4); mean coefficients of the best-fit polynomial and relative uncertainties (5, 6).
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