Inserting the slope inside a log-log chart with pgfplots

Question

I would like to insert the slope inside a log-log chart with pgfplots. I checked both the pgfplots documentation and the net, but I didn't find something helpful about this problem.

Here is the MWE:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5.1}
\usepackage{amsmath,amssymb}
\begin{document}

\begin{tikzpicture}
    \begin{loglogaxis}[
     xlabel={x},
     ylabel={y},
     xmin=0.01, xmax=0.10,
     ymin=200, ymax=750,
     width=.8\columnwidth,
     /pgfplots/log ticks with fixed point,
     /pgfplots/ytick={250,300,400,...,700}]
     ]
     \addplot
     coordinates{
     (0.0090,   704.11)
     (0.0300,   476.05)
     (0.0600,   379.49)
     (0.0900,   332.26)
     (0.1005,   320.46)
     };
     \end{loglogaxis}
\end{tikzpicture}
\end{document}

Answer 1

You can calculate the linear regression to a set of points using the key y={create col/linear regression={y=<column name>}} in the plot options. This allows you to plot a straight line for the slope, and using coordinate [pos=<fraction>] (<name>) you can save points on this line that can be used for drawing a slope triangle.

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots,pgfplotstable}
\pgfplotsset{compat=1.5.1}
\usepackage{amsmath,amssymb}
\begin{document}

\pgfplotstableread{
0.0090  704.11
0.0300  476.05
0.0600  359.49
0.0900  332.26
0.1005  320.46
}\datatable

\begin{tikzpicture}
    \begin{loglogaxis}[
     xlabel={x},
     ylabel={y},
     xmin=0.01, xmax=0.10,
     ymin=200, ymax=750,
     width=.8\columnwidth,
     /pgfplots/log ticks with fixed point,
     /pgfplots/ytick={200,300,...,700}]
     ]
     \addplot [only marks, red] table {\datatable}; % plot the data
     \addplot [black]
        table [y={create col/linear regression={y=1}}] {\datatable} % calculate and plot the regression line
        coordinate [pos=0.25] (A) % save two points on the regression line for drawing the slope triangle
        coordinate [pos=0.4] (B)
     ;
     \xdef\slope{\pgfplotstableregressiona} % save the slope parameter
     \draw (A) -| (B)  % draw the opposite and adjacent sides of the triangle
        node [pos=0.25, anchor=south] {1} % label the horizontal line
        node [pos=0.75,anchor=west] {\pgfmathprintnumber{\slope}} label the vertical line
     ;
     \end{loglogaxis}
\end{tikzpicture}
\end{document}