\begin{table}%t2
\caption{Correlation coefficients ($r$), number of stars used to define the upper
 envelope ($N$), parameters of the linear, exponential and power law  weighted fits
 to the data upper envelope of  $A_{\max}-P$ and $A_{\max}-R_{\rm
 0}$ relations and reduced chi-squares ($\chi^2_{\rm \nu}$).}
\label{tabcoeff}
%\centering
$$
\begin{tabular}{@{\hspace{.1cm}}l@{\hspace{.1cm}}r@{\hspace{.1cm}}|l@{\hspace{.1
cm}}|l@{\hspace{.2cm}}l@{\hspace{.2cm}}l@{\hspace{.1cm}}|l@{\hspace{.1cm}}l@{\hspace{.1cm}}l@{\hspace{.1cm}}|l@{\hspace{.2cm}}l@{\hspace{.2cm}}l@{\hspace{.1cm}}
}
\hline
\hline
Sp. type  &  $r$      &  $N$  &     $a $       &          $b$       &   $\chi^2_{\nu}$ &
   ln($a$)  & $b$ & $\chi^2_{\nu}$ & ln($a$)  & $b$ & $\chi^2_{\nu}$\\
\hline
\multicolumn{2}{c}{} & \multicolumn{10}{c}{} \\
\multicolumn{3}{c}{}  & \multicolumn{3}{c}{$A_{\rm max}$ = $a + bP$} &
 \multicolumn{3}{c}{ln($A_{\rm max}$) = ${\rm ln}(a)+bP$}    &
 \multicolumn{3}{c}{ln(A$_{\rm max}$) = ${\rm ln}(a)+b{\rm ln}(P)$}\\                         
\multicolumn{2}{c}{ultra fast } & \multicolumn{9}{c}{}\\
G0$-$G7 &  $-$0.98  & 5 & 0.23 $\pm$ 0.02 & $-$0.190 $\pm$ 0.040 & 0.05 &
 $-$1.20 $\pm$ 0.02 & $-$1.741 $\pm$ 0.040 & 1.79 & $-$2.73 $\pm$ 0.02 &
 $-$0.849 $\pm$ 0.020 & 16.5\\
G8$-$K5 &  $-$0.98  & 7 & 0.36 $\pm$ 0.02 & $-$0.264 $\pm$ 0.025 & 0.42 &
 $-$0.43 $\pm$ 0.02 & $-$2.045 $\pm$ 0.020 & 7.58 &$-$2.49 $\pm$ 0.01 &
 $-$1.337 $\pm$ 0.017 & 62.1\\
\hline
\multicolumn{2}{c}{fast } &\multicolumn{10}{c}{} \\
F5$-$F9 &  $-$0.89  & 12 & 0.07 $\pm$ 0.01 & $-$0.005 $\pm$ 0.001 &0.24  &
 $-$2.38 $\pm$ 0.01 & $-$0.174 $\pm$ 0.001  & 0.15 & $-$2.42 $\pm$ 0.01 &
 $-$0.625 $\pm$ 0.005 & 0.29\\
G0$-$G7 &  $-$0.99  & 15 & 0.14 $\pm$ 0.01 & $-$0.011 $\pm$ 0.001 &0.22  &
 $-$1.78 $\pm$ 0.01 & $-$0.142 $\pm$ 0.001  & 0.32 & $-$1.63 $\pm$ 0.01 &
 $-$0.607 $\pm$ 0.010 & 1.29\\
G8$-$K5 &  $-$0.91  & 15 & 0.20 $\pm$ 0.01 & $-$0.013 $\pm$ 0.001 &4.27  &
 $-$1.41 $\pm$ 0.01 & $-$0.136 $\pm$ 0.001  & 0.53 & $-$1.18 $\pm$ 0.01 &
 $-$0.668 $\pm$ 0.010 & 1.33\\  
K6$-$M4$^a$     &  $-$0.93  & 10 & 0.17 $\pm$ 0.01 & $-$0.015 $\pm$ 0.003  &0.64  &
 $-$1.54 $\pm$ 0.01 & $-$0.193 $\pm$ 0.003  & 0.71 & $-$1.42 $\pm$ 0.02 &
 $-$0.787 $\pm$ 0.012 & 1.19\\
K6$-$M4$^b$     &  $-$0.92  &  4 & 0.44 $\pm$ 0.02 & $-$0.028 $\pm$ 0.002   &2.63  &
 $-$0.15 $\pm$ 0.02 & $-$0.211 $\pm$ 0.002  & 0.49 & $+$1.84 $\pm$ 0.03  &
 $-$1.885 $\pm$ 0.020 & 0.05\\
\hline
\multicolumn{12}{c}{}\\
\multicolumn{3}{c}{}  &\multicolumn{3}{c}{$A_{\rm max}$ = $a + bR_{\rm 0}$} &
 \multicolumn{3}{c}{ln($A_{\rm max}$) = ${\rm ln}(a)+bR_{\rm 0}$}  &
 \multicolumn{3}{c}{ln($A_{\rm max}$) = ${\rm ln}(a)+b{\rm ln}(R_{\rm 0}$)}\\
\multicolumn{2}{c}{ultra fast} & \multicolumn{7}{c}{}\\
G0$-$G7 & $-$0.98   & 5 & 0.20 $\pm$ 0.02 & $-$2.020 $\pm$ 0.460  & 0.06    &
 $-$1.37 $\pm$ 0.02 & $-$19.250 $\pm$ 0.460 & 2.82 & $-$4.68 $\pm$ 0.06 &
 $-$0.763 $\pm$ 0.019 & 3.47\\
G8$-$K5 & $-$0.95   & 7 & 0.34 $\pm$ 0.02 & $-$5.107 $\pm$ 0.504  & 1.05    &
 $-$0.55 $\pm$ 0.02 &$-$42.031 $\pm$ 0.504 & 2.59 & $-$7.07 $\pm$ 0.06 &
 $-$1.464 $\pm$ 0.018 & 42.9\\ 
\hline
\multicolumn{2}{c}{fast } &\multicolumn{10}{c}{} \\
F5$-$F9  & $-$0.91   & 12 & 0.07 $\pm$ 0.01 & $-$0.036 $\pm$ 0.008 &  0.23  &
 $-$2.34 $\pm$ 0.01 & $-$1.248 $\pm$ 0.009 & 0.07 & $-$3.65 $\pm$ 0.01 &
 $-$0.766 $\pm$ 0.014 & 0.15\\
G0$-$G7  & $-$0.98   & 15 & 0.16 $\pm$ 0.01 & $-$0.169 $\pm$ 0.015 &  0.66  &
 $-$1.51 $\pm$ 0.01 & $-$2.431 $\pm$ 0.014 & 0.98 & $-$3.37 $\pm$ 0.01 &
 $-$0.824 $\pm$ 0.013 & 2.58\\
G8$-$K5  & $-$0.91   & 15 & 0.21 $\pm$ 0.01 & $-$0.286 $\pm$ 0.018 &  2.40  &
 $-$1.36 $\pm$ 0.01 & $-$2.914 $\pm$ 0.018 & 0.42 & $-$3.08 $\pm$ 0.01 &
 $-$0.599 $\pm$ 0.010 & 1.08\\
K6$-$M4$^a$      & $-$0.94   & 10 & 0.17 $\pm$ 0.01 & $-$0.410 $\pm$ 0.070 &  0.60  &
 $-$1.55 $\pm$ 0.01 & $-$5.069 $\pm$ 0.070 & 0.63 & $-$4.02 $\pm$ 0.03 &
 $-$0.796 $\pm$ 0.028 & 1.09\\
K6$-$M4$^b$      & $-$0.94   &  4 & 0.44 $\pm$ 0.02 & $-$0.732 $\pm$ 0.050 &  2.00  &
 $-$0.16 $\pm$ 0.02 & $-$5.462 $\pm$ 0.050 & 0.16 & $-$4.25 $\pm$ 0.02 &
 $-$1.846 $\pm$ 0.039 & 0.03\\
\hline
\multicolumn{5}{l}{$^a$ Upper envelope 1. $^b$ Upper envelope 2.}
\end{tabular}
$$
\end{table}