\documentclass[tikz,border=0.1in]{standalone}

\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}

\usepackage{amssymb, amsmath, amsthm}

\usepackage{pgfplots}
\usepackage{pgfplotstable}

\begin{document}

\begin{tikzpicture}
\begin{axis} [
  ylabel=$\mathrm{ln}(T)$,
  xlabel=$\mathrm{ln}(L)$,
  xmin=-2.1, xmax=-0.9,
  ymin=-0.45, ymax=0.14,
  legend pos = outer north east,
]
  \addplot+ [mark=none] {0.4601*x + 0.5066};
  \addlegendentry {$0.46x + 0.51$};
  \addplot+ [only marks,mark=*,color=blue,mark options={fill=blue}] table [col sep=comma, x index=2, y index=3] {data/var_l.csv};
\end{axis}
\end{tikzpicture}

\end{document}