Cfrgtkky

This is a continuation of this question.

Below is my current output and problematic area is that brown curve.

I am trying to plot pdf as a 2D graph standing upon the regression line (red).

I am able to place it on a specific point, but I want to place upon the linear regression line calculated by tikz, at expected value of Y for a particular x, which would be on the line (Y = ax + b). Since reg line is automatically calculated, I am unable to fetch and place. Is there a way to do that or should I have another table or manual regression line drawn (please also specify how to do that here, if that should be the case)

MWE:

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



% ref: https://tex.stackexchange.com/questions/456138/marks-do-not-appear-in-3d-for-3d-scatter-plot/456142

pgfdeclareplotmark{fcirc}

{%          

          begin{scope}[local frame]

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

                    fill circle(0.1);

              end{scope}   

          end{scope}

}%

newcommand{GetLocalFrame}

{

    path let p1=(     $(1,0,0)-(0,0,0)$   ), p2=(    $(0,1,0)-(0,0,0)$   ), p3=(   $(0,0,1)-(0,0,0)$   )  % these look like axes line paths

    in pgfextra  %pgfextra is to execute below code before constructing the above path 

    {

        pgfmathsetmacro{ratio}

        {   

            veclen(x1,y1)/veclen(x2,y2)  

        }

        globaldefs=1relax   % I think this makes all assignments global

        tikzset

        {

            local frame/.style/.expanded =

            {   

                x   =  {   (x1,y1)    },

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

                z   =   {     (x3,y3)     }

            }

        }

    }; 

}



tikzset

{

    declare function={

            % normal(m,s)=1/(2*s*sqrt(pi))*exp(-(x-m)^2/(2*s^2));

            normal(x,m,s) = 1/(2*s*sqrt(pi))*exp(-(x-m)^2/(2*s^2));

        }

}





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},

        samples=200,

        samples y=0, 

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

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

        clip=false, axis lines = middle,

        area plot/.style=   % for this: https://tex.stackexchange.com/questions/53794/plotting-several-2d-functions-in-a-3d-graph

        {

            fill opacity=0.5,

            draw=none,

            fill=orange,

            mark=none,

            smooth

        }

    ]

    % read out the transformation done by pgfplots



    GetLocalFrame

    begin{scope}[transform shape]

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

    end{scope}



    defX{2.7}

    defY{23}

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

    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) {$E(Y|x_1)=mu_{Y.x_1}$};



    %https://tex.stackexchange.com/questions/254484/how-to-make-a-graph-of-heteroskedasticity-with-tikz-pgf/254497

    addplot3 [area plot, domain=(14-5):(14+5)] (2.2, x, {30*normal(x, 14, 2)});





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}

Not exactly an MWE but my current whole document, as I am building this graph step by step, so you could also know the context to optimize and integrate with existing plot efficiently.

I already referred and referring here and here but already spent too much time trying to integrate as something fails here or there.

Update (problems still exist): For time being, I have managed to draw manual regression line and plotting on that, however, I am unable to draw a single vertical line. I am some how unable to get the peak value of dist to pass as z (instead have passed hardcoded value 5), and also weirdly, the line does not cross the sample behind the curve which gives a weird 3d perspective.

Current output:

MWE:

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



% ref: https://tex.stackexchange.com/questions/456138/marks-do-not-appear-in-3d-for-3d-scatter-plot/456142

pgfdeclareplotmark{fcirc}

{%          

          begin{scope}[local frame]

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

                    fill circle(0.1);

              end{scope}   

          end{scope}

}%

newcommand{GetLocalFrame}

{

    path let p1=(     $(1,0,0)-(0,0,0)$   ), p2=(    $(0,1,0)-(0,0,0)$   ), p3=(   $(0,0,1)-(0,0,0)$   )  % these look like axes line paths

    in pgfextra  %pgfextra is to execute below code before constructing the above path 

    {

        pgfmathsetmacro{ratio}

        {   

            veclen(x1,y1)/veclen(x2,y2)  

        }

        globaldefs=1relax   % I think this makes all assignments global

        tikzset

        {

            local frame/.style/.expanded =

            {   

                x   =  {   (x1,y1)    },

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

                z   =   {     (x3,y3)     }

            }

        }

    }; 

}



tikzset

{

    declare function={

            % normal(m,s)=1/(2*s*sqrt(pi))*exp(-(x-m)^2/(2*s^2));

            normal(x,m,s) = 1/(2*s*sqrt(pi))*exp(-(x-m)^2/(2*s^2));

        }

}





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={130}{50},

        samples=200,

        samples y=0, 

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

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

        clip=false, axis lines = middle,

        area plot/.style=   % for this: https://tex.stackexchange.com/questions/53794/plotting-several-2d-functions-in-a-3d-graph

        {

            fill opacity=0.5,

            draw=none,

            fill=orange,

            mark=none,

            smooth

        }

    ]

    % read out the transformation done by pgfplots



    GetLocalFrame

    begin{scope}[transform shape]

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

    end{scope}



    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) {$E(Y|x_1)=mu_{Y.x_1}$};





    % regression line - lets try to manually calculate

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

    defa{2.62}

    defb{9.85}

    addplot3 [samples=2, samples y=0, red, domain=1:6] (x, {a*(x)+b}, 0);



    % normal distribution above the interesting regression point, that is expected value of Y for a given x

    %https://tex.stackexchange.com/questions/254484/how-to-make-a-graph-of-heteroskedasticity-with-tikz-pgf/254497

    pgfmathsetmacrovalueY{a*(X)+b}

    addplot3 [area plot, domain=0:40)] (X, x, {100*normal(x, valueY, 3)});



    draw [thick] (X,valueY,0) to (X,valueY,5);  %HOW TO GET TO PEAK OF DIST AND ALSO OVER THE BLUE SAMPLE LYING BEHIND THIS LINE



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}

Can you please help? Also how to reduce the font size of axes? They appear too big.

Congratulations to what you've achieved! I find it amazing. The last step is almost trivial in comparison. You know the function you plot, which suggests to just draw draw [thick] (X,valueY,0) to (X,valueY,{100*normal(valueY, valueY, 3)});. As for the background/foreground issue, this can be resolved by adding set layers and drawing the line on the axis foreground (say).

documentclass{article}

usepackage{tikz}

usepackage{pgfplots, pgfplotstable}

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



% 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



% ref: https://tex.stackexchange.com/questions/456138/marks-do-not-appear-in-3d-for-3d-scatter-plot/456142

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)     }

            }

    }; 

}





tikzset

{

    declare function={

            % normal(m,s)=1/(2*s*sqrt(pi))*exp(-(x-m)^2/(2*s^2));

            normal(x,m,s) = 1/(2*s*sqrt(pi))*exp(-(x-m)^2/(2*s^2));

        }

}





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}

    [set layers,   

        view={130}{50},

        samples=200,

        samples y=0, 

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

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

        clip=false, axis lines = middle,

        area plot/.style=   % for this: https://tex.stackexchange.com/questions/53794/plotting-several-2d-functions-in-a-3d-graph

        {

            fill opacity=0.5,

            draw=none,

            fill=orange,

            mark=none,

            smooth

        }

    ]

    % read out the transformation done by pgfplots



    GetLocalFrame

    begin{scope}[transform shape]

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

    end{scope}



    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) {$E(Y|x_1)=mu_{Y.x_1}$};





    % regression line - lets try to manually calculate

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

    defa{2.62}

    defb{9.85}

    addplot3 [samples=2, samples y=0, red, domain=1:6] (x, {a*(x)+b}, 0);



    % normal distribution above the interesting regression point, that is expected value of Y for a given x

    %https://tex.stackexchange.com/questions/254484/how-to-make-a-graph-of-heteroskedasticity-with-tikz-pgf/254497

    pgfmathsetmacrovalueY{a*(X)+b}

    addplot3 [area plot, domain=0:40)] (X, x, {100*normal(x, valueY, 3)});

    pgfonlayer{axis foreground}

    draw [thick] (X,valueY,0) to (X,valueY,{100*normal(valueY, valueY, 3)});  

    endpgfonlayer

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}