\begin{table}%t5 \caption{\label{pearsonvimos_lumi}Linear Pearson correlation coefficients~$r$ and linear fits for for the class~1 and 2~LIRGs distributed in luminosity groups spanning the entire luminosity range.} %%\centering \par \begin{tabular}{ccccccccccccc} \hline \hline \noalign{\smallskip} Luminosity Range & \multicolumn{2}{c}{[N~\textsc{ii}]$\lambda$6584/H$\alpha$} & \multicolumn{2}{c}{[S~\textsc{ii}]$\lambda$6717,6731/H$\alpha$} & \multicolumn{2}{c}{[O~\textsc{i}]$\lambda$6300/H$\alpha$}\\ ($\log(L/L_\odot)$)& $r$ & A+Bx & $r$ & A+Bx & $r$ & A+Bx \\ \hline 11.00--11.25 & 0.49 & --0.97 + 0.39 x & 0.63 & --1.39 + 0.54 x & --0.05 & --1.12 -- 0.09 x\\ 11.25--11.50 & 0.72 & --1.24 + 0.51 x & 0.63 & --1.19 + 0.37 x & 0.68 & --3.09 + 1.01 x\\ 11.50--11.75 & 0.28 & --0.77 + 0.22 x & 0.24 & --0.81 + 0.20 x & 0.35 & --2.47 + 0.61 x\\ 11.75--12.00 & 0.59 & --1.58 + 0.64 x & 0.43 & --1.21 + 0.41 x & 0.46 & --3.01 + 0.95 x \\ \hline \end{tabular} %\vspace*{5mm} \end{table}