Adding borders to an entire row in a table
You can use \tikzmark to place some marks at the desired locations and then draw the frame using the marks; a little example:
\documentclass{article}
\usepackage{tikz}
\usepackage{pdflscape}
\newcommand\tikzmark[1]{%
\tikz[remember picture,overlay] \node (#1) {};}
\begin{document}
\begin{landscape}
\begin{tabular}{rcccccccc|cccccccc}
& \multicolumn{ 8}{c}{section 1} & \multicolumn{ 8}{c}{section 2} \\
& & & & & & & & & & & & & & & & \\
& (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) & (12) & (13) & (14) & (15) & (16) \\
& & & & & & & & & & & & & & & & \\
regression coef 1 & no & no & no & no & no & no & no & no & no & no & no & no & no & no & no & no \\
& & & & & & & & & & & & & & & & \\
\tikzmark{a}regression coef 2 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & & & & & & & & \\
& \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & & & & & & & & \phantom{noo}\tikzmark{b} \\
\end{tabular}
\begin{tikzpicture}[remember picture,overlay]
\draw[line width=1pt,draw=orange!70!black,rounded corners=4pt]
([xshift=-3pt,yshift=7pt]a.north) rectangle ([xshift=3pt,yshift=-5pt]b.south);
\end{tikzpicture}
\end{landscape}
\end{document}
The code needs two runs to stabilize.
As a side note, \bf is a deprecated command; you should use \bfseries instead. Also, the table cells define groups so you don't need to explicitly group using braces.
You can get fancier borders using tikz but the classic way is to us \hline
\documentclass{article}
\usepackage{pdflscape}
\begin{document}
\begin{landscape}
\begin{tabular}{rcccccccc|cccccccc}
& \multicolumn{ 8}{c}{section 1} & \multicolumn{ 8}{c}{section 2} \\
& & & & & & & & & & & & & & & & \\
& (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) & (12) & (13) & (14) & (15) & (16) \\
& & & & & & & & & & & & & & & & \\
regression coef 1 & no & no & no & no & no & no & no & no & no & no & no & no & no & no & no & no \\
& & & & & & & & & & & & & & & & \\
\hline
\multicolumn{1}{|r}{regression coef 2 }& \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & \bfseries 1234 & & & & & & & &\multicolumn{1}{c|}{} \\
\hline
& \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & \bfseries [2] & & & & & & & &
\end{tabular}
\end{landscape}
\end{document}