Description of the data
(taken from the Andrews and Herzberg
book, page 63):
Great Lakes area. The data are taken from the eleven maps listed in
Table 10.2. These maps are believed to be representative of the
period of time commencing with the widespread knowledge that five
major lakes existed in the interior of North America, and ending when
relatively large scale hydrographic surveys of the lakes' shorelines
were being done.
The data shown in Table 10.1 consist of the latitude, [phi], and
longitude, [lambda], co-ordinates, as determined for each map, for
each of 39 points easily identifiable on the eleven maps. These data
were obtained by placing a grid over the old maps and doing a linear
interpolation. Interpolation accuracy is felt to be good except for
the indicated numbers. Also included are the current co-ordinates for
the 39 points.
It is conjectured that there are five key ways a map might be
systematically in error. These are: a constant error in latitude, a
constant error in longitude, a proportional error in latitude, a
proportional error in longitude, and error resulting in a non-zero
angle between true North and the map's North. In addition, groups of
locations, for example, one whole lake, may be off.
The primary task is to develop a methodology for parameterizing each
map with respect to these characteristics and with respect to any
other characteristics that seem to be important
Note: A minus sign indicates that the interpolation accuracy is
not good.
Problem 4
Pick any of the old maps (for example, Coronelli 1688). Draw a plot
of the actual points, as a map. Be sure that you have 'west' pointing
to the left, and that the horizontal axis is labelled with the degrees
west. If you are ambitious, try to superimpose a map of the US (using
the usa() function), so that you can see where the landmarks are.
Problem 5
Draw a plot showing both actual locations and the locations for one of
the oldmaps, with arrows joining each actual point to its location on
the old map. Warning: look at the data for funny values.
Problem 6
(For the real enthusiasts)
Pick an old map. Fit a linear model to both oldmap$lat and
oldmap$long, using actual latitude and longitude as predictors.
Draw a picture showing the actual locations, with arrows attached
indicating the residuals from the linear fits.