Vietnam Draft Numbers

On December 1st, 1969, the first Vietnam draft lottery was held to determine who would be drafted to fight in the Vietnam War. Every man in the country born between 1944 through 1950 was assigned a lottery number based on their date of birth. People with a lower number were called first. Anyone with a lottery number from 1 to 195 was eventually called to serve.

results = read.csv("http://people.hsc.edu/faculty-staff/blins/classes/spring18/math222/data/vietnamDraft.csv")
plot(results$Birthday,results$y69,xlab="Birthdate",ylab="Draft Number",main="1969 Vietnam Draft Lottery")

Shortly after the draft, there was a controversy because the lottery numbers weren’t completely random. The days of the year (including February 29) were written on slips of paper. These pieces of paper were then placed in separate plastic capsules that were mixed in a shoebox and then dumped into a deep glass jar. Capsules were drawn from the jar one at a time. Because of the way they were mixed in the shoebox, there was a bias in the lottery meant that people with birthdays later in the year were more likely to have low draft numbers.

1. Use the data above to find the least squares regression line for finding the 1969 draft number based on Birthday, and show that the slope is significantly different from zero.

2. Did the government fix the problem for the draft lotteries in 1970, 71, and 72?