\begin{table}%t3
\caption {\label{tab5}The values of the Pearson linear $\varrho$ and Kendall rank $\varsigma$ correlation coefficients.}
%\begin{small}
%\centerline
 {\begin{tabular}{ccccc} 
\hline\hline \noalign{\smallskip}            
 & Sal, BC & Sal, M & Cha, BC & Kro, M \\
\noalign{\smallskip} \hline \noalign{\smallskip}
$\varrho [{\rm log_{10}}(R_{{\rm e}}),{\rm log_{10}}(M_{*})]$ & 0.90 ($<$0.01) & 0.84 ($<$0.01) & 0.90 ($<$0.01) & 0.84 ($<$0.01) \\
$\varsigma [R_{{\rm e}},M_{*}]$ & 0.67 ($<$0.01) & 0.60 ($<$0.01) & 0.67 ($<$0.01) & 0.60 ($<$0.01) \\
$\varrho [{\rm log_{10}}(M_{*}/(2\pi~R_{{\rm e}}^2)),{\rm log_{10}}(M_{*})]$ & --0.40 ($<$0.01) & --0.29 (0.03) & --0.43 ($<$0.01) & --0.28 (0.04) \\
$\varsigma [M_{*}/(2\pi~R_{{\rm e}}^2),M_{*}]$ & --0.20 (0.02) & --0.14 (0.14) & --0.21 (0.02) & --0.12 (0.18) \\
%$\varrho [{\rm log_{10}}(D_{1}/\langle D_{1} \rangle),{\rm log_{10}}(L_{B})]$ & 0.33 (0.02) & 0.33 (0.02) & 0.33 (0.02) & 0.33 (0.02) \\
%$\varsigma [D_{1}/\langle D_{1} \rangle,L_{B}]$ & 0.23 (0.01) & 0.23 (0.01) & 0.23 (0.01) & 0.23 (0.01) \\
$\varrho [{\rm log_{10}}(D_{1}/\langle D_{1} \rangle),{\rm log_{10}}(M_{*})]$ & 0.30 (0.03) & 0.24 (0.09) & 0.31 (0.02) & 0.24 (0.09) \\
$\varsigma [D_{1}/\langle D_{1} \rangle,M_{*}]$ & 0.23 (0.02) & 0.14 (0.15) & 0.23 (0.01) & 0.14 (0.15) \\
$\varrho [{\rm log_{10}}(M_{*,0}),{\rm log_{10}}(M_{*,0}L_{B,0}^{-1})]$ & 0.74 ($<$0.01) & 0.65 ($<$0.01) & 0.72 ($<$0.01) & 0.64 ($<$0.01) \\
$\varsigma [M_{*,0},M_{*,0}L_{B,0}^{-1}]$ & 0.57 ($<$0.01) & 0.46 ($<$0.01) & 0.56 ($<$0.01) & 0.49 ($<$0.01) \\
%$\varrho [{\rm log_{10}}(L_{B,0}),{\rm log_{10}}(M_{*,0}L_{B,0}^{-1})]$ & 0.58 ($<$0.01) & 0.36 ($<$0.01) & 0.55 ($<$0.01) & 0.35 ($<$0.01) \\
%$\varsigma [L_{B,0},M_{*,0}L_{B,0}^{-1}]$ & 0.43 ($<$0.01) & 0.28 ($<$0.01) & 0.42 ($<$0.01) & 0.30 ($<$0.01) \\
$\varrho [z_{l},{\rm log_{10}}(M_{*}L_{B}^{-1})-{\rm log_{10}}(M_{*,0}L_{B,0}^{-1})]$ & $-$0.87 ($<$0.01) & $-$0.87 ($<$0.01) & $-$0.90 ($<$0.01) & $-$0.88 ($<$0.01) \\
$\varsigma [z_{l},{\rm log_{10}}(M_{*}L_{B}^{-1})-{\rm log_{10}}(M_{*,0}L_{B,0}^{-1})]$ & $-$0.69 ($<$0.01) & $-$0.75 ($<$0.01) & $-$0.74 ($<$0.01) & $-$0.76 ($<$0.01) \\
$\varrho \{ {\rm log_{10}}[M_{*}({\le} R_{{\rm Ein}})],{\rm log_{10}}[M_{{\rm tot}}^{{\rm len}}(\le R_{{\rm Ein}})] \}$ & 0.92 ($<$0.01) & 0.87 ($<$0.01) & 0.93 ($<$0.01) & 0.87 ($<$0.01) \\
$\varsigma [M_{*}({\le} R_{{\rm Ein}}),M_{{\rm tot}}^{{\rm len}}({\le} R_{{\rm Ein}})]$ & 0.74 ($<$0.01) & 0.68 ($<$0.01) & 0.74 ($<$0.01) & 0.69 ($<$0.01) \\
\noalign{\smallskip} \hline
\end{tabular}}
\smallskip
Notes: For the different models and IMFs, the values of the correlation coefficients between the specified variables are given. In parentheses, we show the probabilities that an equal number of measurements of two uncorrelated variables would give values of the coefficients higher than the measured ones.
\end{table}