[Tex/LaTex] add a trend line to this plot

pgfplots

I have this graph:

\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.9}
\usepackage{filecontents}
\begin{filecontents*}{data.csv}
a,b
1.230448921,0.460822919
1.342422681,0.694747354
1.431363764,0.828862164
1.505149978,0.993514561
1.568201724,1.257457266
1.62324929,1.521115401
1.672097858,1.822516751
1.716003344,2.125021632
1.755874856,2.355223203
1.792391689,2.567059417
1.826074803,2.763380773
1.857332496,2.932403886
1.886490725,3.081848588
1.913813852,3.208627804
1.939519253,3.324555792
\end{filecontents*}

\begin{filecontents*}{test.csv}
a,b
1.230448921,0.460822919
1.230448921,0.694747354
1.342422681,0.694747354
1.342422681,0.828862164
1.431363764,0.828862164
1.431363764,0.993514561
1.505149978,0.993514561
1.505149978,1.257457266
1.568201724,1.257457266
1.568201724,1.521115401
1.62324929,1.521115401
1.62324929,1.822516751
1.672097858,1.822516751
1.672097858,2.125021632
1.716003344,2.125021632
1.716003344,2.355223203
1.755874856,2.355223203
1.755874856,2.567059417
1.792391689,2.567059417
1.792391689,2.763380773
1.826074803,2.763380773
1.826074803,2.932403886
1.857332496,2.932403886
1.857332496,3.081848588
1.886490725,3.081848588
1.886490725,3.208627804
1.913813852,3.208627804
1.913813852,3.324555792
1.939519253,3.324555792
\end{filecontents*}

\begin{document}
\begin{tikzpicture}
\begin{loglogaxis}[
    title = log-log,
    xlabel={$x$},
    ylabel={$y$},
]
\addplot[blue] table [x=a,y=b,col sep=comma] {test.csv};
\end{loglogaxis}
\end{tikzpicture}
\end{document}

That gives the following graph:

enter image description here

I would like to add a trend line in red from the data in data.csv and display the equation. I am new to latex. In test.csv, I simply modified the coordinates to have the steps; is there a more elegant way of plotting points as series of steps? Thank you very much for your time!

Best Answer

Load pgfplotstable (which loads pgfplots too) and read the test.csv as, say, \datatable. Then you can add 

\addplot[red] table[
    y={create col/linear regression={y=b}}
]{\datatable};

to plot the trend line. The slope and intercept of the trend line are stored in \pgfplotstableregressiona and \pgfplotstableregressionb respectively. You can add a legend for the trendline forming an equation like

\addlegendentry{%
$\pgfmathprintnumber{\pgfplotstableregressiona} \cdot x
\pgfmathprintnumber[print sign]{\pgfplotstableregressionb}$}

Code:

\documentclass{standalone}
\usepackage{pgfplotstable}
\pgfplotsset{width=10cm,compat=1.9}
\usepackage{filecontents}
\begin{filecontents*}{test.csv}
a,b
1.230448921,0.460822919
1.230448921,0.694747354
1.342422681,0.694747354
1.342422681,0.828862164
1.431363764,0.828862164
1.431363764,0.993514561
1.505149978,0.993514561
1.505149978,1.257457266
1.568201724,1.257457266
1.568201724,1.521115401
1.62324929,1.521115401
1.62324929,1.822516751
1.672097858,1.822516751
1.672097858,2.125021632
1.716003344,2.125021632
1.716003344,2.355223203
1.755874856,2.355223203
1.755874856,2.567059417
1.792391689,2.567059417
1.792391689,2.763380773
1.826074803,2.763380773
1.826074803,2.932403886
1.857332496,2.932403886
1.857332496,3.081848588
1.886490725,3.081848588
1.886490725,3.208627804
1.913813852,3.208627804
1.913813852,3.324555792
1.939519253,3.324555792
\end{filecontents*}

\begin{document}
\pgfplotstableread[col sep=comma]{test.csv}\datatable
\begin{tikzpicture}
\begin{loglogaxis}[
    title = log-log,
    xlabel={$x$},
    ylabel={$y$},
]
\addplot[blue] table [x=a,y=b,col sep=comma] {\datatable};
\addplot[red] table[
    y={create col/linear regression={y=b}}
]
{\datatable};
\addlegendentry{Data}
\addlegendentry{%
$\pgfmathprintnumber{\pgfplotstableregressiona} \cdot x
\pgfmathprintnumber[print sign]{\pgfplotstableregressionb}$}
\end{loglogaxis}
\end{tikzpicture}
\end{document}

enter image description here

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