4

The picture shows a normal linear regression.

Although it is easy to compute on paper, I have no idea how to code a linear regression in order to get an output shown as in the picture.

I would be very pleased if anyone could help me.

I have already tried {tikzpicture} etc. but it does not work out that good as pleased.

enter image description here

  • 8
    Welcome to TeX.SE! Please edit your question and add a minimal example of what you tried. – CarLaTeX Dec 1 '18 at 13:07
  • 1
    pgfplots allows you to do this, see p 396 Fitting Lines - Regression: ctan.org/pkg/pgfplots – AndréC Dec 1 '18 at 13:15
  • 1
    @CarLaTeX think a little before you get carried away! Rebecca wants to know how she can create this graph. If she knew, she wouldn't have asked that question. – AndréC Dec 1 '18 at 13:39
  • 1
    @AndréC Rebecca wrote "I have already tried...". Did you read the entire post? – CarLaTeX Dec 1 '18 at 14:38
  • 2
    Pleqee, edit the question title to reflect the inquiry of drawing a linear regression graph out of raw data. This will help future readers coming from relevant Google search results. – Diaa Dec 2 '18 at 15:43
6

mwe

With R and knitr this plot is relatively simple. However, the MWE is a bit complex to show automatically the actual coefficients (intercept, slope and error) as well as to place legend, arrow and label automatically, so one can change the values at some range (for instance, the second y from 2 to -3) and still have a correct output in all aspects, even in the text out of the figure.

\documentclass{article}
\usepackage{lipsum}
\usepackage[german]{babel}
\usepackage[utf8]{inputenc}

<<Daten,echo=F>>=
df <- data.frame(x=c(1,2,3,3,4,5),y=c(1,2,6,7,10,8))
@
\begin{document}
\lipsum[2]
<<Streudiagramm,echo=F,dev="tikz", fig.cap="Regressionszeile zeigt den Fehler $\\varepsilon_2$", fig.width=4.2, fig.height=3.5,fig.align='center',fig.pos="h">>=
par(mar=c(4,4,1,4)) # optional, just to crop
mod <- lm(df$y~df$x)
with(df,plot(x,y, pch=21, col="red",bg="yellow",ylim=c(min(df$y-.1),max(df$y+.1))))
abline(mod,col="blue",lwd=3)
legend(1, max(df$y), legend=c("$f(x_i)=\\beta_0+\\beta_1x_i$",
   paste("$y=",
         signif(mod$coefficients[1],3),"+",
         signif(mod$coefficients[2],3),"x$")),
       col=c("blue","white"), lty=1:2, cex=0.8)
arrows(df$x[2],df$y[2],df$x[2],predict(mod)[2], length=0.05, col =2, code=3)
text(df$x[2]+.1,mean(c(df$y[2],predict(mod)[2])),paste('Str\\"{o}erm: $\\varepsilon_i=y_i-f(x_i)$ =',signif(df$y[2]-predict(mod)[2],3)),adj=0)
@

Die Abbildung  \ref{fig:Streudiagramm} zeigt das  $\varepsilon_2 = 
\Sexpr{signif(df$y[2],3)} - 
\Sexpr{signif(predict(mod)[2],3)} =  
\Sexpr{signif(df$y[2]-(mod$coefficients[1]+(mod$coefficients[2]*df$x[2])),3)} $. 
\lipsum[3]
\end{document}
13

Motivated by AndréC's comments... ;-)

\documentclass{article}
\usepackage{tikzlings}
\usepackage{pgfplots, pgfplotstable}

\pgfplotsset{compat=1.16}
\pgfplotstableread{
X Y 
1 2
2 2.5
3 6
3 6.5
4 10
5 8
}\datatable


\begin{document}
\pgfplotsset{every axis legend/.append style={
        cells={anchor=west}}}

\begin{tikzpicture}
\begin{axis}[legend pos=north west,xmin=0,xmax=7,
ymin=0,ymax=15,enlargelimits=0.1]

    \addplot[only marks, mark=*] table[x=X,y=Y] {\datatable};
 \addlegendentry{$y_i$}

 \addplot[draw=none,color=red] table [
      x=X,
      y={create col/linear regression={y=Y}},
 ] {\datatable};
 \xdef\slope{\pgfplotstableregressiona}
 \xdef\offset{\pgfplotstableregressionb}
 \addplot[no marks,color=red,domain=-2:9] {\slope*x+\offset};
 \addlegendentry{$f(x_i)=\beta_0+\beta_1x_i$}
 \coordinate (aux1) at (2,{\slope*2+\offset});
 \coordinate (aux2) at (2,2.5);
\end{axis}
\draw[latex-latex,red] (aux1) -- (aux2)
node[midway,right,text=black,font=\sffamily]{St\"orterm:
$\varepsilon_i=y_i-f(x_i)$};
\marmot[xshift=8cm,whiskers,teeth,crystal ball]
\end{tikzpicture}
\end{document}

enter image description here

And this is motivated by Sebastiano's comment.

\documentclass{article}
\usepackage{tikzlings}
\usepackage{pgfplots, pgfplotstable}

\pgfplotsset{compat=1.16}
\pgfplotstableread{
X Y 
1 2
2 2.5
3 6
3 6.5
4 10
5 8
}\datatable

% pgfmanual p. 1087
\pgfdeclareradialshading{ballshading}{\pgfpoint{-10bp}{10bp}}
 {color(0bp)=(cyan!15!white); color(9bp)=(cyan!75!white);
 color(18bp)=(cyan!70!black); color(25bp)=(cyan!50!black); color(50bp)=(black)}

\pgfdeclareplotmark{crystal ball}{\pgfpathcircle{\pgfpoint{0ex}{0ex}}{1ex}
  \pgfshadepath{ballshading}{0}
  \pgfusepath{}}

\begin{document}
\pgfplotsset{every axis legend/.append style={
        cells={anchor=west}}}

\begin{tikzpicture}
\begin{axis}[legend pos=north west,xmin=0,xmax=7,
ymin=0,ymax=15,enlargelimits=0.1]

    \addplot[only marks, mark=crystal ball,opacity=0.7] table[x=X,y=Y] {\datatable};
 \addlegendentry{$y_i$}

 \addplot[draw=none,color=red] table [
      x=X,
      y={create col/linear regression={y=Y}},
 ] {\datatable};
 \xdef\slope{\pgfplotstableregressiona}
 \xdef\offset{\pgfplotstableregressionb}
 \addplot[no marks,color=red,domain=-2:9] {\slope*x+\offset};
 \addlegendentry{$f(x_i)=\beta_0+\beta_1x_i$}
 \coordinate (aux1) at (2,{\slope*2+\offset});
 \coordinate (aux2) at (2,2.5);
\end{axis}
\draw[latex-latex,red] (aux1) -- (aux2)
node[midway,right,text=black,font=\sffamily]{St\"orterm:
$\varepsilon_i=y_i-f(x_i)$};
\marmot[xshift=8cm,whiskers,teeth,crystal ball]
\end{tikzpicture}
\end{document}

enter image description here

  • Off topic, but how did you make the little bear on the right hand side? It is very cute! :) Just another tikzpicture? In particular, how did roughly you make that ball with varying translucency? – Danny Dan Dec 1 '18 at 18:31
  • 2
    @DanHoynoski Which bear??? Do you see a bear here? You can find bears here, even with crystal balls (and indeed this is just a ball shading with some nontrivial opacity). But I insist that the "little bear" is a "cute marmot". ;-) – user121799 Dec 1 '18 at 18:40
  • It would be good to improve the title of the question to say that it is a question of building a normal linear regression. – AndréC Dec 1 '18 at 23:03
  • @AndréC I guess that is more a request to the OP. You may refer to this question to motivate the request. (I won't do that as long as the OP does not confirm that this is what she's after.) – user121799 Dec 1 '18 at 23:07
  • 3
    @AndréC The OP can always comment on their own question – Joseph Wright Dec 2 '18 at 9:34

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