# Set up

I'm replicating a simple correlation scatter graph with a random set of nodes given as follows:

# MWE

I have my MWE as follows which have the graphs set up as to the scale that i think it is in the book:

\documentclass[11pt, oneside]{book}

%pakages for figures
\usepackage[labelfont=bf]{caption}
\usepackage{float}
\usepackage{graphicx}

%pakage for graph
\usepackage{tikz}

\usepackage{amsmath}
\usepackage{amssymb}

%--------------------------------BEGIN--------------------
\begin{document}

\begin{figure}[H]
\centering
\begin{minipage}{0.32\textwidth}
\centering
\begin{tikzpicture}
\draw[->,ultra thick] (-1.7,0)--(1.7,0) node[right]{$x$};
\draw[->,ultra thick] (0,-1.7)--(0,1.7) node[above]{$y$};
\end{tikzpicture}
\caption{a) Possetive Correlation}\label{CORA}
\end{minipage}\hfill
\begin{minipage}{0.32\textwidth}
\centering
\begin{tikzpicture}
\draw[->,ultra thick] (-1.7,0)--(1.7,0) node[right]{$x$};
\draw[->,ultra thick] (0,-1.7)--(0,1.7) node[above]{$y$};
\end{tikzpicture}
\caption{b) Uncorrelated/No Correlation}\label{CORB}
\end{minipage}\hfill
\begin{minipage}{0.32\textwidth}
\centering
\begin{tikzpicture}
\draw[->,ultra thick] (-1.7,0)--(1.7,0) node[right]{$x$};
\draw[->,ultra thick] (0,-1.7)--(0,1.7) node[above]{$y$};
\end{tikzpicture}
\caption{c) Negative Correlation}\label{CORC}
\end{minipage}\hfill
\end{figure}

\end{document}


# Goal

I'm asking for on how to actually plot the points. I know how to do this if it was a simple function, but how would you do this for a random collection of nodes.

You can draw a sequence of points along the x-axis with random y-coordinates in the pictures. For the different graphs you can use the x-value and add a random component (positive correlation), use the inverse of the x-value and add a random component (negative correlation) or keep it completely random (no correlation).

In the MWE below first the coordinates are computed and then a correction is performed in case the random coordinate would be outside of the graph (e.g., a random x-coordinate of -1.8 is corrected to -1.7). The random engine is seeded with \pgfmathsetseed to get a different result on every compilation.

You can change the numbers in the foreach loop to get a different amount of points and the division of the random numbers can be changed to increase/decrease randomness (i.e., correlation).

Code:

\documentclass[11pt, oneside]{book}

%pakages for figures
\usepackage[labelfont=bf]{caption}
\usepackage{float}
\usepackage{graphicx}

%pakage for graph
\usepackage{tikz}
\usetikzlibrary{calc}
\pgfmathsetseed{\number\pdfrandomseed}

\usepackage{amsmath}
\usepackage{amssymb}

%--------------------------------BEGIN--------------------
\begin{document}

\begin{figure}[H]
\centering
\begin{minipage}{0.32\textwidth}
\centering
\begin{tikzpicture}
\draw[->,ultra thick] (-1.7,0)--(1.7,0) node[right]{$x$};
\draw[->,ultra thick] (0,-1.7)--(0,1.7) node[above]{$y$};
\foreach \x in {-1.7,-1.5,...,1.7}{
\pgfmathsetmacro\xcoord{\x+rand/10}
\pgfmathsetmacro\ycoord{\x+rand/2}
\pgfmathsetmacro\xcoord{\xcoord < -1.7 ? -1.7 : \xcoord}
\pgfmathsetmacro\xcoord{\xcoord > 1.7 ? 1.7 : \xcoord}
\pgfmathsetmacro\ycoord{\ycoord < -1.7 ? -1.7 : \ycoord}
\pgfmathsetmacro\ycoord{\ycoord > 1.7 ? 1.7 : \ycoord}
\node[circle,draw,fill=black,scale=0.3] at (\xcoord,\ycoord) {};
}
\end{tikzpicture}
\caption{a) Positive Correlation}\label{CORA}
\end{minipage}\hfill
\begin{minipage}{0.32\textwidth}
\centering
\begin{tikzpicture}
\draw[->,ultra thick] (-1.7,0)--(1.7,0) node[right]{$x$};
\draw[->,ultra thick] (0,-1.7)--(0,1.7) node[above]{$y$};
\foreach \x in {-1.7,-1.5,...,1.7}{
\pgfmathsetmacro\xcoord{\x+rand/10}
\pgfmathsetmacro\ycoord{rand*2}
\pgfmathsetmacro\xcoord{\xcoord < -1.7 ? -1.7 : \xcoord}
\pgfmathsetmacro\xcoord{\xcoord > 1.7 ? 1.7 : \xcoord}
\pgfmathsetmacro\ycoord{\ycoord < -1.7 ? -1.7 : \ycoord}
\pgfmathsetmacro\ycoord{\ycoord > 1.7 ? 1.7 : \ycoord}
\node[circle,draw,fill=black,scale=0.3] at (\xcoord,\ycoord) {};
}
\end{tikzpicture}
\caption{b) Uncorrelated/No Correlation}\label{CORB}
\end{minipage}\hfill
\begin{minipage}{0.32\textwidth}
\centering
\begin{tikzpicture}
\draw[->,ultra thick] (-1.7,0)--(1.7,0) node[right]{$x$};
\draw[->,ultra thick] (0,-1.7)--(0,1.7) node[above]{$y$};
\foreach \x in {-1.7,-1.5,...,1.7}{
\pgfmathsetmacro\xcoord{\x+rand/10}
\pgfmathsetmacro\ycoord{-\x+rand/2}
\pgfmathsetmacro\xcoord{\xcoord < -1.7 ? -1.7 : \xcoord}
\pgfmathsetmacro\xcoord{\xcoord > 1.7 ? 1.7 : \xcoord}
\pgfmathsetmacro\ycoord{\ycoord < -1.7 ? -1.7 : \ycoord}
\pgfmathsetmacro\ycoord{\ycoord > 1.7 ? 1.7 : \ycoord}
\node[circle,draw,fill=black,scale=0.3] at (\xcoord,\ycoord) {};
}
\end{tikzpicture}
\caption{c) Negative Correlation}\label{CORC}
\end{minipage}\hfill
\end{figure}

\end{document}


Possible result:

• Its very interesting this approach. For figure 2: I've notice that on compiling, it will generate a different position of points ever single time. Is there any way to permanently fix the positions once I've found a pattern that i like?? – UniStuffz Jan 4 '18 at 16:25
• @UniStuffz that is possible, see, e.g., tex.stackexchange.com/questions/387814/… (in short: at the start, after initialization of the random seed, retrieve the value of the seed and print it, so you can set this specific value as a seed at a later time). – Marijn Jan 4 '18 at 18:06

And an example of an alternative approach with Metapost:

\RequirePackage{luatex85}
\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
vardef signum(expr x) =
if x > 0: 1 elseif x < 0: -1 else: 0 fi
enddef;

vardef random_correlates(expr N, R, S) =
save r; numeric r;
% r = R clipped to -1 < r < 1
r = if R > 1: 1 elseif R < -1: -1 else: R fi;

save p; picture p;
p = image(
drawarrow (-S-4, 0) -- (S+4, 0); label.rt("$x$", (S+4,0));
drawarrow (0, -S-4) -- (0, S+4); label.top("$y$", (0, S+4));

for x=-S step 2S/N until S:
drawdot (x, (abs r)[-S + uniformdeviate 2S, x*signum(r)])
withpen pencircle scaled 2
withcolor 2/3 blue;
endfor

label.bot("$r=" & decimal r & "$", (0,-S-4));
);
p
enddef;

beginfig(1);
draw random_correlates(24,  0.7, 42);
draw random_correlates(24, -0.7, 42) shifted 120 right;
draw random_correlates(24,  0,   42) shifted 240 right;
endfig;

\end{mplibcode}
\end{document}


Notes:

• This is wrapped up in luamplib, so compile this with the lualatex engine (or work out how to adapt it for pdflatex + GMP, or plain MP, or Context etc)

• Parameters: N = the number of points to draw, R the desired correlation coefficient, S the semi-scale of the diagram

The clever bit is working out the y-coordinate for the drawdot. In stages (from right to left):

• the signum function is a simple implementation of the standard function to return -1 for negative numbers and +1 for positive, so x*signum(r) gives +x or -x or 0 depending on the value of r.

• uniformdeviate 2S gives a random number in the range 0 < y < 2S, and then adding -S to this gives us -S < y < S.

• I then use the mediation notation with abs(r) to find a number that is somewhere between this completely random y and +x or -x.

So r=1 will map each y to x, r=-1 will map each y to -x, and r=0 will map each y to a completely random value between -S and S (which is what we want).

• This code is incredible and the result is very clean. I haven't even heard of the concepts you have used. I will bow down and say as it stands this code is beyond me (so much so that on copying this into share latex, it does not compile). However this looks exciting and I will look into it, thankyou. – UniStuffz Jan 6 '18 at 14:45
• My example compiles on ShareLatex for me: you need to click on the Menu at the top left, then set the Compiler option to "LuaLaTeX". – Thruston Jan 6 '18 at 20:21

A PSTricks solution only for emergency purpose.

\documentclass[preview,border=12pt]{standalone}
\usepackage{pst-plot}
\pstVerb{realtime srand}
\psset{unit=2mm}
\begin{document}
\noindent
\begin{pspicture}(-6.25,-6.25)(6.5,6.5)
\psLoop{50}{{\psset{linecolor=red}\qdisk(!.5 Rand sub 8 mul dup 1 mul .5 Rand sub 2 mul add){1pt}}}
\psaxes[ticks=none,labels=none]{->}(0,0)(-5,-5)(5,5)[$x$,0][$y$,90]
\end{pspicture}
\begin{pspicture}(-6.25,-6.25)(6.5,6.5)
\psLoop{50}{{\psset{linecolor=red}\qdisk(!.5 Rand sub 8 mul dup -1 mul .5 Rand sub 2 mul add){1pt}}}
\psaxes[ticks=none,labels=none]{->}(0,0)(-5,-5)(5,5)[$x$,0][$y$,90]
\end{pspicture}
\begin{pspicture}(-6.25,-6.25)(6.5,6.5)
\psLoop{50}{{\psset{linecolor=red}\qdisk(!.5 dup Rand sub 8 mul exch Rand sub 8 mul){1pt}}}
\psaxes[ticks=none,labels=none]{->}(0,0)(-5,-5)(5,5)[$x$,0][$y$,90]
\end{pspicture}
\end{document}