# Math 4650: Final Project solution

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## Description

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In November of 1969, with the Vietnam War raging, President Nixon
signed an executive order instructing the Selective Service to reinstitute the
draft. The order stipulated that the selection be a random process based
on the birthdays of men born between January 1, 1944 and December 31,
1950.

The order did not specifically state how the birthdays should be selected. The days of the year (including February 29) were written on slips of
paper. The Selective Service placed these pieces of paper 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. On December 1, 1969,
Rep. Alexander Pirnie, R-NY, drew the first capsule that contained the number 258 corresponding to the date September 14, so all registrants with that
birthday were assigned lottery number 1. The second number drawn was 115
corresponding to April 24, and so forth. All men of draft age (born between
January 1, 1944 and December 31, 1950) who shared a birth date would be
called to serve at once.

The first 195 birthdates drawn were later called to
serve in the order they were drawn; the last of these was September 24. The
fairness of the draft lottery was immediately criticized. Critics contended
that the lottery process was not truly random.

The task of this project is to analyze the data set available on canvas.
The file name is 1970lottery.csv. You have been asked to provide a statistical
analysis of the data and write a brief report on your findings and conclusions.

Your analysis and report should include at least the following parts:
1. Plot draft number versus day number. Do you see any trend
from this scatter plot?

2. Fit a simple linear regression of draft number on day number.
To assess if the simple linear regression model is appropriate for
the draft lottery data, plot the residuals and obtain the Q-Q plot
of the residuals.

3. Does your analysis suggest that your fitte model is appropriate? If not, can you find a suitable transformation that improves
the model in part 2?

4. Provide side-by-side boxplots of draft number for each month.
How do you interpret your findings from these boxplots?

5. To test if the mean draft number for each month is the
same for all months, perform the analysis of variance and related
multiple comparisons (if you deem necessary) for the draft lottery
data.

You may work on this project by yourself or in a group of not
exceeding 3 people. Your written report should be typed not to
exceed 6 pages. Please hand in one report for the group signed by all members. Each group member will receive the same grade and will be assumed
to have participated fully in the project.
Your project must be submitted online in a pdf format to our