Vrftjkry

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.

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};

 xdefslope{pgfplotstableregressiona}

 xdefoffset{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}

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};

 xdefslope{pgfplotstableregressiona}

 xdefoffset{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}

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}