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\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}
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