documentclass[border=5pt]{standalone}
usepackage{xcolor}
usepackage{tikz,pgfplots,pgfplotstable}
%
begin{document}
centering
pgfplotsset{every  major tick/.style={black,},minor y tick num=1}
pgfplotstableread{slope-data.dat}datatable
%
begin{tikzpicture}[scale=1.4]
begin{loglogaxis}[
axis background/.style={
shade,top color=gray!60,bottom color=white},
legend style={fill=white,font=scriptsize, at={(0.96,0.10)},anchor=south east},
tick label style={font=scriptsize},
label style={font=footnotesize},
legend cell align=left,
xlabel={$a$},
ylabel={$N(a)$},
legend entries={$r = 0.50-M=2^{0}$, $ d_mathrm{f} = pgfmathprintnumber{slope} pm $},
]
%
addplot+[mark=halfcircle*,only marks,every mark/.append style={rotate=90}]
table[font=scriptsize] {main-data.dat};
%
addplot+[mark=x,mark repeat=5,mark phase=6,smooth]
table[y={create col/linear regression={y=1}}]{datatable}
coordinate [pos=0.3] (A)
coordinate [pos=0.69] (B);
% store slope
xdefslope{pgfplotstableregressiona}
draw [red,thick] (A) |- (B)
node[anchor=east,font=scriptsize,red] at (3.33,7.8)  {$sim$pgfmathprintnumber{slope}};
%
end{loglogaxis}
end{tikzpicture}
%
end{document}