Draw multiple horizontal Gaussian bells shifted ik TikZ

Question

I would like to create something like this to illustrate linear models. Here is my code so far, generated using Mathcha, just to have an idea of what I would like.

\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-0.75,xscale=0.75]
        %uncomment if require: \path (0,300); %set diagram left start at 0, and has height of 300
    %Shape: Axis 2D [id:dp8361200068338723]
    \draw  (50,250.04) -- (610.41,250.04)(106.04,11.54) -- (106.04,276.54) (603.41,245.04) -- (610.41,250.04) -- (603.41,255.04) (101.04,18.54) -- (106.04,11.54) -- (111.04,18.54)  ;
    %Straight Lines [id:da4842290347914763]
    \draw [color={rgb, 255:red, 74; green, 144; blue, 226 }  ,draw opacity=1 ]   (551.41,21.04) -- (44.91,263.54) ;
    %Curve Lines [id:da2882365205325442]
    \draw [fill={rgb, 255:red, 126; green, 211; blue, 33 }  ,fill opacity=1 ]   (172,159.74) .. controls (181.41,184.64) and (210.41,154.64) .. (219.41,178.64) .. controls (228.41,202.64) and (197.91,206.64) .. (204.91,226.64) ;
    %Curve Lines [id:da35238413522248413]
    \draw [fill={rgb, 255:red, 126; green, 211; blue, 33 }  ,fill opacity=1 ]   (284,107.24) .. controls (293.41,132.14) and (322.41,102.14) .. (331.41,126.14) .. controls (340.41,150.14) and (309.91,154.14) .. (316.91,174.14) ;
    %Curve Lines [id:da8161792691558291]
    \draw [fill={rgb, 255:red, 126; green, 211; blue, 33 }  ,fill opacity=1 ]   (403,51.74) .. controls (412.41,76.64) and (441.41,46.64) .. (450.41,70.64) .. controls (459.41,94.64) and (428.91,98.64) .. (435.91,118.64) ;

    % Text Node
    \draw (112.5,19.4) node [anchor=north west][inner sep=0.75pt]    {$y$};
    % Text Node
    \draw (584,250.9) node [anchor=north west][inner sep=0.75pt]    {$z_{1}$};
    % Text Node
    \draw (538.5,30.9) node [anchor=north west][inner sep=0.75pt]  [font=\footnotesize,color={rgb, 255:red, 74; green, 144; blue, 226 }  ,opacity=1 ]  {$y=\beta _{0} +\beta _{1} z_{1}$};
    % Text Node
    \draw (537.5,67.74) node [anchor=north west][inner sep=0.75pt]  [font=\footnotesize] [align=left] {$\displaystyle \forall z_{i}$ prendo \\valori \textcolor[rgb]{0.49,0.83,0.13}{qui dentro}};
\end{tikzpicture}

I know how to generate axis and lines in pure TikZ (i.e. without Mathcha), but I have no idea on how to do for the Gaussian bells.

Well, what is the mathematical representation of that Gaussian Bell curve? Is it just two Bézier curves or does it need to be plotted (and what is its function)? If you have that you just shift and rotate your coordinate system. — Qrrbrbirlbel, Mar 14 '23 at 09:09

score 5 · Accepted Answer · answered Mar 14 '23 at 09:13

As Qrrbrbirlbel says in the comments you only need to plot the gaussian curve and shift it, rotate it and scale it as you need.

A starting point could be:

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[line cap=round,scale=2]
\coordinate (A) at (-0.5,-0.1);
\draw[-stealth] (-0.5,0) -- (5,0)  node[below] {$z_1$};
\draw[-stealth] (0,-0.5) -- (0,3)  node[left]  {$y$};
\draw[blue]     (A)    --++ (30:6) node[below right] {$y=\beta_0+\beta_1z_1$};
\node[text width=3cm,right] at (4.7,2) {$\forall z_1$ prendo\valori \textcolor{green}{qui dentro}};
\foreach\i in {1.5,3,4.5}
  \draw[shift={($(A)+(30:\i)$)},scale=0.4,rotate=-60,fill=green] plot[domain=-1.5:1.5,samples=41] (\x,{exp(-2\x\x)});
\end{tikzpicture}
\end{document}

Draw multiple horizontal Gaussian bells shifted ik TikZ

1 Answers1