In Mathematica 6 and later there is a special function, Inset, for that purpose.
Here is a simple, realistic example. The residuals of a fit are the differences between the data and the fitted curve.
Data Initialization
In[1]:= dat = {{0, 1.28086}, {1, 1.56017}, {2, 1.91442}, {3, 2.09588}, {4, 2.41924},
{5, 2.37783}, {6, 2.57325}, {7, 2.58195}, {8, 2.43806}, {9, 2.34434},
{10, 2.12974}};
Fit to a Line In[2]:= linfitmodel = b*x + c;
In[3]:= linfitparams = FindFit[dat, linfitmodel, {b, c}, x]
Out[3]= {b->0.0916195,c->1.69788}
In[4]:= linfitresids = dat - Table[{0, linfitmodel /. linfitparams}, {x, 0, 10}];
In[5]:= Show[ListPlot[dat, PlotStyle -> Directive[Red, PointSize]],
Plot[Evaluate[linfitmodel /. linfitparams], {x, 0, 10}],
Graphics[Inset[
ListLinePlot[linfitresids, ImageSize -> 100, PlotLabel -> "Residuals"],
{8, 1.5}]],
AxesOrigin -> {0, 1}, PlotRange -> All]
The residuals curve shows structure - down at the ends and high in the middle.
This suggests that a higher-order term might be useful. Fit to a Quadratic Curve In[6]:= quadfitmodel = a*x^2 + b*x + c;
In[7]:= quadfitparams = FindFit[dat, quadfitmodel, {a, b, c}, x]
Out[7]= {a->-0.0309372,b->0.400991,c->1.23382}
In[8]:= quadfitresids = dat - Table[{0, quadfitmodel /. quadfitparams}, {x, 0, 10}];
In[9]:= Show[ListPlot[dat, PlotStyle -> Directive[Red, PointSize]],
Plot[Evaluate[quadfitmodel /. quadfitparams], {x, 0, 10}],
Graphics[Inset[
ListLinePlot[quadfitresids, ImageSize -> 100, PlotLabel -> "Residuals"],
{8, 1.5}]],
AxesOrigin -> {0, 1}, PlotRange -> All]
The residuals are small and random, which suggests a decent fit. In[1]:= ?Inset
Inset[obj] represents an object obj inset in a graphic.
Inset[obj, pos] specifies that the inset should be placed at
position pos in the graphic.
Inset[obj, pos, opos] aligns the inset so that position opos
in the object lies at position pos in the enclosing graphic.
Inset[obj, pos, opos, size] specifies the size of the inset in the
coordinate system of the enclosing graphic.
Inset[obj, pos, opos, size, dirs] specifies that the axes of the
inset should be oriented in directions dirs.
