\begin{table}%t3
%\centering
\par
\caption{Best-fit results on the scaling relations corrected by the cosmological
factor $E_z$
(dashed and dotted lines in the plots; see Eq.~(\ref{eq:fit})).
The temperature, $T_{\rm gas, 6}$, is in unit of 6~keV;
the luminosity, $L_{\rm bol, 44}$, in $10^{44}~ h_{70}^{-2}$~erg~s$^{-1}$;
the total mass, $M_{\rm tot, 14}$, in $10^{14}~ h_{70}^{-1}~ M_{\odot}$;
the gas mass, $M_{\rm gas, 13}$, in $10^{13}~ h_{70}^{-5/2} ~M_{\odot}$.
When the slope~$A$ is fixed, we estimate the error-weighted mean
of $(\log Y -A \log X)$ and evaluate the error after resampling~$Y$ and~$X$
by~1000 times according to their uncertainties.
The scatter on~$Y$ is measured as $\left[ \sum_{j=1,N}   
\left(\log Y_j -\alpha -A \log X_j \right)^2 /N \right]^{1/2}$.
Note that the scatter along the $X$-axis can be estimated as
$\sigma_{\log X} = \sigma_{\log Y} / A$.\label{tab:fit}} 
\begin{tabular}{l@{\hspace{.7em}} c@{\hspace{.7em}} c@{\hspace{.7em}} c@{\hspace{.7em}} }
 \hline \hline 
 Relation $(Y-X)$ & $\alpha$ & $A$ & $\sigma_Y$ \\ 
 \hline 
 $E_z^{-1} L_{\rm bol, 44}-T_{\rm gas, 6}$ & $0.79 (\pm0.07)$ & $3.72 (\pm0.47)$ & $0.35$ \\ 
 & $1.00 (\pm0.02)$ & $2.00$ (fixed) & $0.41$ \\ 
 $E_z M_{\rm tot, 14}-T_{\rm gas, 6}$ & $0.75 (\pm0.03)$ & $1.98 (\pm0.30)$ & $0.15$ \\ 
 & $0.74 (\pm0.02)$ & $1.50$ (fixed) & $0.15$ \\ 
 \noalign{\smallskip}
 $E_z M_{\rm gas, 13}-T_{\rm gas, 6}$ & $0.79 (\pm0.03)$ & $2.37 (\pm0.24)$ & $0.17$ \\ 
 & $0.92 (\pm0.01)$ & $1.50$ (fixed) & $0.22$ \\ 
 \noalign{\smallskip}
 $E_z^{-1} L_{\rm bol, 44}- E_z M_{\rm tot, 14}$ &$-0.63 (\pm0.32)$ & $1.88 (\pm0.42)$ & $0.47$ \\ 
 & $0.09 (\pm0.03)$ & $1.33$ (fixed) & $0.52$ \\ 
 \hline 
\end{tabular}
\end{table}