## Illustrative Example

Suppose we have a series of data obtained from an experiment that measure position (x) versus time (t) of a particle that moves with constant velocity. The data can be stored in a file named result.dat and **saved in the same folder of your main project**.

t x 0 1 1.2 1.78 2.3 4.495 3.4 5.21 4.1 4.665 5.6 5.64 6.5 7.225 7.2 7.68 8.1 6.265 9.3 8.045 10.7 8.955

## Plot data from a file in LaTeX

**To plot this data in LaTeX, we can use the \addplot command along with the table option **and **specify the name of the columns **we want to plot, like follows:

\documentclass{standalone} % Required package \usepackage{pgfplots} \usepackage{pgfplotstable} \pgfplotsset{compat = newest} \begin{document} \begin{tikzpicture} \begin{axis}[ xmin = 0, xmax = 11, ymin = 0, ymax = 11, width = \textwidth, height = 0.75\textwidth, xtick distance = 1, ytick distance = 1, grid = both, minor tick num = 1, major grid style = {lightgray}, minor grid style = {lightgray!25}, ] % plot data line code \addplot[teal, only marks] table[x = t, y = x] {result.dat}; \end{axis} \end{tikzpicture} \end{document}

Compiling the above code yields:

Notice that in the preamble we have included the **pgfplotstable package. ****This package allows us to use the table command**, and more important, it will help us to **compute the linear regression for our data**. In the previous code, we have also included some extra options in the axis environment that **changes the style of the grid**, the **limits of the plots**. Also notice that in the \addplot command we have included the **only marks options to get a scatter plot**. For more details, I invite you to read this post about plotting functions and data in LaTeX.

## Compute and Plot Linear Regression in LaTeX

Now here comes the interesting part. Usually to plot a linear regression we use third party software like Excel. But **with the pgfplotstable package we can compute the linear fitting inside the LaTeX document**. We just need to add the next sentence to the code:

\addplot[options] table[

x = column_name,

y = {create col/linear regression = {y = column_name}}

] {data_file_name.dat};

Here we specify the name of the column in the x axis, in our case it should be t, and for the values for the y axis we pass the command create col/linear regression, which computes a linear regression for the data_file_name.dat.

**The next code shows how to implement the code to plot the line that better fits the whole scatter data**:

\documentclass{standalone} % Required package \usepackage{pgfplots} \usepackage{pgfplotstable} \pgfplotsset{compat = newest} \begin{document} \begin{tikzpicture} \begin{axis}[ xmin = 0, xmax = 11, ymin = 0, ymax = 11, width = \textwidth, height = 0.75\textwidth, xtick distance = 1, ytick distance = 1, grid = both, minor tick num = 1, major grid style = {lightgray}, minor grid style = {lightgray!25}, xlabel = {Time ($t$)}, ylabel = {Position ($x$)}, legend cell align = {left}, legend pos = north west ] % Plot data \addplot[ teal, only marks ] table[x = t, y = x] {result.dat}; % Linear regression \addplot[ thick, orange ] table[ x = t, y = {create col/linear regression={y=x}} ] {result.dat}; % Add legend \addlegendentry{Data} \addlegendentry{ Linear regression: $ x = \pgfmathprintnumber{\pgfplotstableregressiona} \cdot t \pgfmathprintnumber[print sign]{\pgfplotstableregressionb}$ }; \end{axis} \end{tikzpicture} \end{document}

**Comments: **

Now we can see the trend line plotted. But that's not the most important feature of the **pgfplotstable package**. In this situations **it's not only important to plot the trend line, but also to find its equation**.

It's well known that **the equation of a linear regression looks like**:

x = a\cdot t + b

Now we need to **compute the constants a and b**. The **slope parameter a can be computed using the following command**:

\pgfmathprintnumber{\pgfplotstableregressiona}

And **to compute b we use:**

\pgfmathprintnumber[print sign]{\pgfplotstableregressionb}

** The \pgfplotstableregressiona and \pgfplotstableregressionb commands returns the values for the constants a and b respectively. **

For our illustrative example, we got:

x = 0.69\cdot t + 1.87

Which r**epresents the movement equation of the particle**.