有人可以制作这个图形，但具有同方差性吗？

Question

下面令人惊叹的优雅图表来自这个帖子。有人能帮我画出同样的图表，但要具有同方差性（而不是异方差性）吗？也许吧杰克? 谢谢你，杰克，谢谢你的原创。

Answer 1

根据维基百科当你询问同方差性时，你似乎想要宽度不变的高斯分布。这可以通过对杰克的精彩回答。

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\pgfdeclareplotmark{dot}
{%
    \fill circle [x radius=0.02, y radius=0.08];
}%

\begin{document}

\begin{tikzpicture}[ % Define Normal Probability Function
declare function={
            normal(\x,\m,\s) = 1/(2*\s*sqrt(pi))*exp(-(\x-\m)^2/(2*\s^2));
        },
    declare function={invgauss(\a,\b) = sqrt(-2*ln(\a))*cos(deg(2*pi*\b));}
       ]
\begin{axis}[
    %no markers,
    domain=0:12,
    zmin=0, zmax=1,
    xmin=0, xmax=3,
    samples=200,
   samples y=0,
    view={40}{30},
    axis lines=middle,
    enlarge y limits=false,
    xtick={0.5,1.5,2.5},
    xmajorgrids,
    xticklabels={},
    ytick=\empty,
    xticklabels={$x_1$, $x_2$, $x_3$},
    ztick=\empty,
    xlabel=$x$, xlabel style={at={(rel axis cs:1,0,0)}, anchor=west},
    ylabel=$y$, ylabel style={at={(rel axis cs:0,1,0)}, anchor=south west},
    zlabel=Probability density, zlabel style={at={(rel axis cs:0,0,0.5)}, rotate=90, anchor=south},
    set layers, mark=cube
  ]

\addplot3 [gray!50, only marks, mark=dot, mark layer=like plot, samples=200,
domain=0.1:2.9, on layer=axis background] (x, {1.5*(x-0.5)+3+invgauss(rnd,rnd)}, 0);
\addplot3 [samples=2, samples y=0, domain=0:3] (x, {1.5*(x-0.5)+3}, 0);
\addplot3 [cyan!50!black, thick] (0.5, x, {normal(x, 3, 0.75)});
\addplot3 [cyan!50!black, thick] (1.5, x, {normal(x, 4.5, 0.75)});
\addplot3 [cyan!50!black, thick] (2.5, x, {normal(x, 6, 0.75)});

\begin{pgfonlayer}{axis background}
\draw [gray, on layer=axis background] (0.5, 3, 0) -- (0.5, 3, {normal(0,0,0.75)}) (0.5,0,0) -- (0.5,12,0)
    (1.5, 4.5, 0) -- (1.5, 4.5, {normal(0,0,0.7)}) (1.5,0,0) -- (1.5,12,0)
    (2.5, 6, 0) -- (2.5, 6, {normal(0,0,0.75)}) (2.5,0,0) -- (2.5,12,0);

\end{pgfonlayer}
\end{axis}
\end{tikzpicture}
\end{document}