In 1970, Congress instituted a lottery for the military draft to support the unpopular war in Vietnam. All 366 possible birth dates were placed in plastic capsules in a rotating drum and were selected one by one. Eligible males born on the first day drawn were first in line to be drafted, etc. The results were criticized by some who claimed that government incompetency at running a fair lottery resulted in a tendency of men born later in the year being more likely to be drafted. Indeed, later investigation revealed that the birth dates were placed in the drum by month and were not thoroughly mixed. The columns of the file 1970lottery are month, month number, day of the year, and draft number.
a. Plot draft number versus day number. Do you see any trend?
b. Plot the linear regression line on the scatterplot.
c. Plot a local linear smoothing on the scatterplot. Try varying the bandwidth.
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