\begin{table}%t6
%\centering
\par
\caption{\label{coef_correl}Linear correlation coefficients and probability for a chance correlation between the pair of parameters plotted in Figs.~\ref{comparison_all} and~\ref{comparison_low}.}
\begin{tabular}{ccccc}
\hline\hline \noalign{\smallskip}
Physical parameter & Linear correlation & Number of  &  Probability for       & Linear fit    \\ 
vs. Log($L_\odot$)     & coefficient        & objects     &   a chance correlation & slope        \\
\hline 
Log($\alpha$)       & 0.12 & 107 & 1.  & -- \\
Log($R_{\rm out}$)      & 0.90 & 60 & 10$^{-20}$  &  0.3 \\
Log($M_{\rm env}$)      & 0.96 & 46 & 10$^{-22}$   & 1.3 \\
Log($n_{1000~{\rm AU}}$)    & 0.72 & 56 & 10$^{-8}$   & 0.3 \\
Log($\langle n \rangle $)     & 0.25 & 39 & 0.4   & -- \\
Log($n_{10{\rm K}}$)    & --0.26 & 18 & 0.5   &  -- \\
Log($\theta$) &  0.88     & 60    &  10$^{-19}$ & --$6 \times 10^{-3}$   \\
\hline
\end{tabular}
\end{table}