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\documentclass{scrartcl} 
\usepackage[T1]{fontenc} 
\usepackage[utf8]{inputenc} 
\usepackage[ngerman]{babel} 
\usepackage{pgfplots,pgfplotstable} 
\pgfplotsset{compat=1.9}
\usepackage[locale=DE]{siunitx} 
\usepackage{filecontents} 

\begin{filecontents*}{Aufgabe_8.2.dat} 
 U I 
 0 0 
 2 2 
 5 5 
\end{filecontents*} 

\begin{document} 
\begin{tikzpicture}
\begin{axis}[
 axis x line=bottom,   
 xmin=0, 
 xmax=7, 
 axis y line=left, 
 ymin=0, 
 ymax=7, 
 xlabel={$U$ in $\left[\si{\volt}\right]$}, 
 ylabel={$I$ in$\left[\si{\micro\ampere}\right]$}] 
\addplot[smooth] table [y={create col/linear regression={y=I}}] {Aufgabe_8.2.dat};
\draw[-, line width =1pt](axis cs:2,2) -- (axis cs:2,0);  
\end{axis} 
\end{tikzpicture} 
\end{document} 

\documentclass[11pt,fleqn]{scrartcl}


\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage{tikz}
\usepackage{pgfplots,pgfplotstable} 
\usepackage[locale=DE]{siunitx} 
\usepackage{gnuplottex}
\usepackage{filecontents} 

\begin{filecontents*}{Aufgabe_8.2.dat} 
U I 
0 0 
2 2
5 5
\end{filecontents*}

\begin{document}
\begin{tikzpicture}[scale=1]
\begin{axis}[ 
axis x line=bottom,  
xmin=0, 
xmax=7,
axis y line=left, 
ymin=0,
ymax=7,
xlabel={$U$ in $\left[\si{\volt}\right]$}, 
ylabel={$I$ in$\left[\si{\micro\ampere}\right]$}] 
%\addplot+[only marks, mark=x, color=black] table {Aufgabe_8.2.dat}; 
\addplot[smooth] table [y={create col/linear regression={y=I}}] {Aufgabe_8.2.dat}; 
\end{axis} 
\draw[-, line width =1pt](2,2) -- (2,0);
\draw[help lines,step=0.25, line width=0.01pt](0,0) grid (7,7);
\end{tikzpicture} 
\end{document}