Graphics Reference
In-Depth Information
Figure
.
.
Contour plot of Galton's smoothed data, showing the curves of y
x (filled circles, solid line),
x
y (open circles, solid line) and the corresponding regression lines (dashed)
treated in more detail in Friendly and Denis (
). Galton's famous graph show-
ing these relations (Fig.
.
) portrays the joint frequency distribution of the height
of children and the average height of their parents. It was produced from a 'semi-
graphic table' in which Galton averaged the frequencies in each set of four adjacent
cells, drew isocurves of equal smoothed value and noted that these formed 'concen-
tric and similar ellipses.'
A literal transcription of Galton's method, using contour curves of constant av-
erage frequency and showing the curves of the means of y
y,isshownin
Fig.
.
.Itis not immediately clear that the contours are concentric ellipses, northat
the curves of means are essentially linear and have horizontal and vertical tangents
to the contours.
A modern data analyst following the spirit of Galton's method might substitute
a smoothed bivariate kernel density estimate for Galton's simple average of adjacent
cells. he result, using jittered points to depict the cell frequencies, and a smoothed
loess curve to show
x and x
isshowninFig.
.
.hecontoursnowdo emphati-
cally suggest concentric similar ellipses, and the regression line is near the points
of vertical tangency. A reasonable conclusion from these figures is that Galton did
not slavishly interpolate isofrequency values as is done in the contour plot shown in
E(
y
x
)
