Story Name: Massachusetts Lunatics
Datafile Name: Massachusetts Lunatics
Abstract:
The data are from a 1854 study involving the percentage of lunatics cared
for at home and a number of associated factors for 14 counties in Massachusetts.   
A study of the relationship between  the percentage of lunatics cared for at home
and distance to the nearest health center is not linear but the relation to the 
reciprocal of distance is essentially linear. In viewing this data  the observer 
should keep in mind that Suffolk County includes Boston, the largest  population
center in the state, that Berkshire is the westernmost county in the state, and that
Duke County (Martha's Vineyard) and Nantucket are islands offshore.

Nantucket is a clear outlier to the pchome vs distance relationship as well as the 
relation to the reciprocal of distance. It is best indexed with an indicator (or dummy)
variable. The student might also look at the pchome vs population density relation.
Note that population density and distance are highly correlated.

Hunter comments that  "Jarvis' discovery  and exposition of distance decay in hospital
sevrices remains important today. The commission recommended that numerous small
mental hospitals be erected at scattered locations rather than huge centralized
facilities." (See Datafile reference and description.) Remember that regression methods
were not formalized until 30-40 years after 1854.