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I would like to create this graph :

Population regression function

So I started with this :

    Clear[droite, norm1, norm2, norm3, hsGPA, graphdroite];

droite[hsGPA_] := 1.5 + 0.5*hsGPA

norm1 = Rotate[Plot[PDF[NormalDistribution[droite@4,.05], y], {y, 2, 6}, 
    PlotRange -> All, Axes -> False], 270 Degree];

norm2 = Rotate[Plot[PDF[NormalDistribution[droite@6,.05], y], {y, 4, 8}, 
    PlotRange -> All, Axes -> False], 270 Degree];

norm3 = Rotate[Plot[PDF[NormalDistribution[droite@8,.05], y], {y, 6, 10}, 
    PlotRange -> All, Axes -> False], 270 Degree];

graphdroite = Plot[droite[hsGPA], {hsGPA, 0, 10}]

Show[graphdroite, norm1, norm2, norm3]

But the Show function doesn't work here.

Any suggestions?

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3 Answers 3

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with Inset 

  Plot[x, {x, 0, 1}, Epilog ->
      Table[
       Inset[Plot[Exp[-x^2], {x, -2, 2}, Axes -> {True, False}],
         {x, x}, {0, 0}, .25, {0, 1}], {x, .25, .75, .25}]]

enter image description here

( actually I'm pretty sure this is a dup but cant find it readily )

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5
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I really don't like the way that Rotate effects Graphics objects. You can't combine them with other Graphics objects since they now have the Head Rotate.

If you are making a y-axis plot, just use ParametricPlot instead:

ParametricPlot[{{y, 1.5 + .5 y},
  {3 + Exp[-(y - 5)^2/5], .2 y + 2.5},
  {6 + Exp[-(y - 5)^2/5], .2 y + 4}
  }, {y, 0, 10}, PlotStyle -> ColorData[97][1]]

Mathematica graphics

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2
  • $\begingroup$ Ok thanks, that looks neat. But would you know how to have the normal plots starting at a different horizontal level? I mean like in the picture I linked with the question. $\endgroup$
    – E Bassal
    Aug 24, 2016 at 20:42
  • $\begingroup$ @EBassal Have a look at the documentation for ParametricPlot, you should be able to make it work. $\endgroup$
    – Jason B.
    Aug 24, 2016 at 21:02
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I've used gaussians here, but this should give you one idea of how to proceed. 

    x0 = {2, 4, 7};
    y0 = {2, 4, 8};
    σ = {1.2, 1, 0.5};
    Show[
     ParametricPlot[
      Evaluate[
       {#1 + Exp[-y^2/#3], y + #2} & @@@ Transpose@{x0, y0, σ}
       ]
      , {y, -2*Max[σ], 2*Max[σ]}
      , PlotStyle -> Blue
      , AspectRatio -> 1/2
      , PlotRange -> {{0, 10}, {0, 10}}
      , LabelStyle -> Directive[FontSize -> 14]
      , Ticks -> {MapIndexed[{#1, "x" <> ToString@First@#2} &, x0], None}
      , AxesLabel -> {None, "y"}
      , ImageSize -> 400
      ]
     , Plot[x, {x, 0, 10}, PlotStyle -> Blue]
     ]

Which gives:

enter image description here

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