Cfrgtkky

I am trying a 3d scatter plot as below, however marks are circles, appearing only in 2D always whichever view I choose. I want them to be flat on the X-Y plane. Please let me know how to do it. I tried "set layers" but that is pushing my entire graph down, behind next section's text. I think even the red line does the same, not giving me proper 3d perspective.

MWE:

documentclass{article}

usepackage{tikz}

usepackage{pgfplots, pgfplotstable}

usetikzlibrary{math, decorations.pathreplacing,angles,quotes,bending, arrows.meta}

pgfplotsset{compat=1.15}

pgfplotstableread{

X Y Z m

2.2 14 0 0

2.7 23 0 0

3 13 0 0

3.55 22 0 0

4 15 0 0

4.5 20 0 0

4.75 28 0 0

5.5 23 0 0

}datatable



makeatletter

        pgfdeclareplotmark{dot}

        {%

            fill circle [x radius=0.02, y radius=0.08];

        }%

makeatother



begin{document}



section{table using raw data in 3D}



The below diagram tries to replicate in 3D, the Figure 12.3 found in cite{devore} , page 472 \



% https://tex.stackexchange.com/questions/11251/trend-line-or-line-of-best-fit-in-pgfplots

begin{tikzpicture}[scale=1.5]

begin{axis}

    [   

    view={140}{50},

    xmin=1,xmax=6, ymin=5,ymax=40, zmin=0, zmax=10,

    % ytick=empty,xtick=empty,ztick=empty,

    clip=false, axis lines = middle

    ]

    addplot3[only marks, fill=cyan,mark=*] table {datatable};

    addplot3[thick, red] table[y={create col/linear regression={y=Y}}] {datatable}; % compute a linear regression from the input table



    defX{2.7}

    defY{23}

    draw [-{Latex[length=4mm, width=2mm]}] (X,Y+10,12.5) node[right]{$(x_1,y_1)$} ..controls (0,5) .. (X,Y,0);

    draw [-{Latex[length=4mm, width=2mm]}] (9,30,20) node[left, align=right]{scriptsize True Regression Line\ scriptsize $y = beta_0 + beta_1 x$} .. controls (5,2.5) .. (5,22.7,0); 

    draw [decorate, decoration={brace,amplitude=3pt}, xshift=0.5mm] (X,Y-0.1,0) to (X,17,0) node[left, xshift=5mm, yshift=-1mm]{scriptsize 1}; % brace 



    draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (1,17.1) to (X,17.1);

    draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (X,17.1) -- (X,5);

    node[above] at (X,4) {$x_1$};

    node[right, align=left,yshift=0.5mm] at (1,17.1) {$E(Y|x_1)=mu_{Y.x_1}$};



end{axis}

end{tikzpicture}









  begin{thebibliography}{1}

  bibitem{devore} Jay. L Devore {em Probability and Statistics for Engineering and the Sciences} 8th Edition.

  end{thebibliography}





end{document}

Output:

UPDATE: A version without hardcoded values. (Note that I use a not entirely harmless command: globaldefs. The alternative will be longer. I believe that here using globaldefs is OK.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{pgfplots, pgfplotstable}

usetikzlibrary{3d,calc,decorations.pathreplacing,arrows.meta}

% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799

makeatletter

tikzoption{canvas is xy plane at z}{%

    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%

    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%

    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%

    tikz@canvas@is@plane}

makeatother

pgfplotsset{compat=1.15}

pgfplotstableread{

X Y Z m

2.2 14 0 0

2.7 23 0 0

3 13 0 0

3.55 22 0 0

4 15 0 0

4.5 20 0 0

4.75 28 0 0

5.5 23 0 0

}datatable

pgfplotstableread{

X Y Z m

2.2 0 0 0

2.7 0 0 0

3 13 0 0

3.55 0 0 0

4 15 0 0

4.5 0 0 0

4.75 0 0 0

5.5 0 0 0

}datatabletwo





pgfdeclareplotmark{fcirc}{%          

          begin{scope}[expand style={local frame}{MyLocalFrame},local frame]

          begin{scope}[canvas is xy plane at z=0,transform shape]

            fill circle(0.1);

          end{scope}   

          end{scope}

}%

% based on https://tex.stackexchange.com/a/64237/121799

tikzset{expand style/.code n args={2}{tikzset{#1/.style/.expanded={#2}}}}

newcommand{GetLocalFrame}{

    path let p1=($(1,0,0)-(0,0,0)$), p2=($(0,1,0)-(0,0,0)$),

    p3=($(0,0,1)-(0,0,0)$) in pgfextra{

    pgfmathsetmacro{ratio}{veclen(x1,y1)/veclen(x2,y2)}

    xdefMyLocalFrame{   

                x   =  {   (x1,y1)    },

                y   =  {    (ratio*x2,ratio*y2)     },

                z   =   {     (x3,y3)     }

            }

    }; }



begin{document}

begin{tikzpicture}[scale=1.5]

begin{axis}

    [   

    view={140}{50},

    xmin=1,xmax=6, ymin=5,ymax=40, zmin=0, zmax=10,

    % ytick=empty,xtick=empty,ztick=empty,

    clip=false, axis lines = middle

    ]

    % read out the transformation done by pgfplots

    GetLocalFrame

    begin{scope}[transform shape]

    addplot3[only marks, fill=cyan,mark=fcirc] 

    table {datatable};

    end{scope}

    addplot3[thick, red] table[y={create col/linear regression={y=Y}}] {datatable}; % compute a linear regression from the input table



    defX{2.7}

    defY{23}

    draw [-{Latex[length=4mm, width=2mm]}] (X,Y+10,12.5) node[right]{$(x_1,y_1)$} ..controls (0,5) .. (X,Y,0);

    draw [-{Latex[length=4mm, width=2mm]}] (9,30,20) node[left, align=right]{scriptsize True Regression Line\ scriptsize $y = beta_0 + beta_1 x$} .. controls (5,2.5) .. (5,22.7,0); 

    draw [decorate, decoration={brace,amplitude=3pt}, xshift=0.5mm] (X,Y-0.1,0) to (X,17,0) node[left, xshift=5mm, yshift=-1mm]{scriptsize 1}; % brace 



    draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (1,17.1) to (X,17.1);

    draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (X,17.1) -- (X,5);

    node[above] at (X,4) {$x_1$};

    node[right, align=left,yshift=0.5mm] at (1,17.1) {$E(Y|x_1)=mu_{Y.x_1}$};



end{axis}

end{tikzpicture}

end{document}

Old ANSWE: This is not an answer but just to show you what you get if do the projection.

documentclass{article}

usepackage{tikz}

usepackage{pgfplots, pgfplotstable}

usetikzlibrary{3d,calc}

% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799

makeatletter

tikzoption{canvas is xy plane at z}{%

    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%

    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%

    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%

    tikz@canvas@is@plane}

makeatother

pgfplotsset{compat=1.15}

pgfplotstableread{

X Y Z m

2.2 14 0 0

2.7 23 0 0

3 13 0 0

3.55 22 0 0

4 15 0 0

4.5 20 0 0

4.75 28 0 0

5.5 23 0 0

}datatable

pgfplotstableread{

X Y Z m

2.2 0 0 0

2.7 0 0 0

3 13 0 0

3.55 0 0 0

4 15 0 0

4.5 0 0 0

4.75 0 0 0

5.5 0 0 0

}datatabletwo



%makeatletter

        pgfdeclareplotmark{dot}

        {%

            fill circle [x radius=0.02, y radius=0.08];

        }%

%makeatother



        pgfdeclareplotmark{fcirc}

        {%

          begin{scope}[x={(-21.20514pt,-9.26361pt)},

          y={(2.54181pt,-1.57715pt)},z={(0.0pt,6.04706pt)}]

          begin{scope}[canvas is xy plane at z=0,transform shape]

            fill circle(0.1);

          end{scope}   

          end{scope}

        }%





begin{document}



section{table using raw data in 3D}



The below diagram tries to replicate in 3D, the Figure 12.3 found in cite{devore} , page 472 \



% https://tex.stackexchange.com/questions/11251/trend-line-or-line-of-best-fit-in-pgfplots

begin{tikzpicture}[scale=1.5]

begin{axis}

    [   

    view={140}{50},

    xmin=1,xmax=6, ymin=5,ymax=40, zmin=0, zmax=10,

    % ytick=empty,xtick=empty,ztick=empty,

    clip=false, axis lines = middle

    ]

    % read out the transformation done by pgfplots

    path let p1=($(1,0,0)-(0,0,0)$), p2=($(0,1,0)-(0,0,0)$),

    p3=($(0,0,1)-(0,0,0)$) in pgfextra{typeout{

    x1,y1;x2,y2;x3,y3}}; 

    begin{scope}[transform shape]

    addplot3[only marks, fill=cyan,mark=fcirc] 

    table {datatable};

    end{scope}

    addplot3[thick, red] table[y={create col/linear regression={y=Y}}] {datatable}; % compute a linear regression from the input table



    defX{2.7}

    defY{23}

%     draw [-{Latex[length=4mm, width=2mm]}] (X,Y+10,12.5) node[right]{$(x_1,y_1)$} ..controls (0,5) .. (X,Y,0);

%     draw [-{Latex[length=4mm, width=2mm]}] (9,30,20) node[left, align=right]{scriptsize True Regression Line\ scriptsize $y = beta_0 + beta_1 x$} .. controls (5,2.5) .. (5,22.7,0); 

%     draw [decorate, decoration={brace,amplitude=3pt}, xshift=0.5mm] (X,Y-0.1,0) to (X,17,0) node[left, xshift=5mm, yshift=-1mm]{scriptsize 1}; % brace 

% 

%     draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (1,17.1) to (X,17.1);

%     draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (X,17.1) -- (X,5);

%     node[above] at (X,4) {$x_1$};

%     node[right, align=left,yshift=0.5mm] at (1,17.1) {$E(Y|x_1)=mu_{Y.x_1}$};



end{axis}

end{tikzpicture}









  begin{thebibliography}{1}

  bibitem{devore} Jay. L Devore {em Probability and Statistics for Engineering and the Sciences} 8th Edition.

  end{thebibliography}





end{document}

The circles are now properly projected on the x-y plane but, unfortunately, since the x and y scales look very different, they look like ellipse. Is that what you want?

On the other hand, if you want to cancel out the elliptic distortion, you can do that by cheating:

documentclass{article}

usepackage{tikz}

usepackage{pgfplots, pgfplotstable}

usetikzlibrary{3d,calc,decorations.pathreplacing,arrows.meta}

% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799

makeatletter

tikzoption{canvas is xy plane at z}{%

    deftikz@plane@origin{pgfpointxyz{0}{0}{#1}}%

    deftikz@plane@x{pgfpointxyz{1}{0}{#1}}%

    deftikz@plane@y{pgfpointxyz{0}{1}{#1}}%

    tikz@canvas@is@plane}

makeatother

pgfplotsset{compat=1.15}

pgfplotstableread{

X Y Z m

2.2 14 0 0

2.7 23 0 0

3 13 0 0

3.55 22 0 0

4 15 0 0

4.5 20 0 0

4.75 28 0 0

5.5 23 0 0

}datatable

pgfplotstableread{

X Y Z m

2.2 0 0 0

2.7 0 0 0

3 13 0 0

3.55 0 0 0

4 15 0 0

4.5 0 0 0

4.75 0 0 0

5.5 0 0 0

}datatabletwo



%makeatletter

        pgfdeclareplotmark{dot}

        {%

            fill circle [x radius=0.02, y radius=0.08];

        }%

%makeatother



        pgfdeclareplotmark{fcirc}

        {%

          begin{scope}[x={(-21.20514pt,-9.26361pt)},

          y={(7.73369*2.54181pt,-7.73369*1.57715pt)},z={(0.0pt,6.04706pt)}]

          begin{scope}[canvas is xy plane at z=0,transform shape]

            fill circle(0.1);

          end{scope}   

          end{scope}

        }%





begin{document}



section{table using raw data in 3D}



The below diagram tries to replicate in 3D, the Figure 12.3 found in cite{devore} , page 472 \



% https://tex.stackexchange.com/questions/11251/trend-line-or-line-of-best-fit-in-pgfplots

begin{tikzpicture}[scale=1.5]

begin{axis}

    [   

    view={140}{50},

    xmin=1,xmax=6, ymin=5,ymax=40, zmin=0, zmax=10,

    % ytick=empty,xtick=empty,ztick=empty,

    clip=false, axis lines = middle

    ]

    % read out the transformation done by pgfplots

    path let p1=($(1,0,0)-(0,0,0)$), p2=($(0,1,0)-(0,0,0)$),

    p3=($(0,0,1)-(0,0,0)$) in pgfextra{

    pgfmathsetmacro{ratio}{veclen(x1,y1)/veclen(x2,y2)}

    typeout{

    x1,y1;x2,y2;x3,y3;ratio}}; 

    begin{scope}[transform shape]

    addplot3[only marks, fill=cyan,mark=fcirc] 

    table {datatable};

    end{scope}

    addplot3[thick, red] table[y={create col/linear regression={y=Y}}] {datatable}; % compute a linear regression from the input table



    defX{2.7}

    defY{23}

    draw [-{Latex[length=4mm, width=2mm]}] (X,Y+10,12.5) node[right]{$(x_1,y_1)$} ..controls (0,5) .. (X,Y,0);

    draw [-{Latex[length=4mm, width=2mm]}] (9,30,20) node[left, align=right]{scriptsize True Regression Line\ scriptsize $y = beta_0 + beta_1 x$} .. controls (5,2.5) .. (5,22.7,0); 

    draw [decorate, decoration={brace,amplitude=3pt}, xshift=0.5mm] (X,Y-0.1,0) to (X,17,0) node[left, xshift=5mm, yshift=-1mm]{scriptsize 1}; % brace 



    draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (1,17.1) to (X,17.1);

    draw [thick,dash pattern={on 7pt off 2pt on 1pt off 3pt}] (X,17.1) -- (X,5);

    node[above] at (X,4) {$x_1$};

    node[right, align=left,yshift=0.5mm] at (1,17.1) {$E(Y|x_1)=mu_{Y.x_1}$};



end{axis}

end{tikzpicture}









  begin{thebibliography}{1}

  bibitem{devore} Jay. L Devore {em Probability and Statistics for Engineering and the Sciences} 8th Edition.

  end{thebibliography}





end{document}

Unfortunately, because of the way pgfplots works, you need to run this, find out the transformation and the "cheating scale" ratio, and then plug this in the definition of fcircle in case you make any changes.