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# Regression Project

For AQR
by

## Alexis Kerman

on 4 January 2013

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#### Transcript of Regression Project

photo (cc) Malte Sörensen @ flickr Regression Project Problem: The crime in Detroit is awful. In 2012, 530,000 people were killed due to gun wounds. Later that year, the took away guns. People no longer had the right to bear arms. Ignoring the anger of the citizens, crime rate decreased 25% each year. Questions.... 1. How many people die in 2036? (25 years later)
2. When will the number of deaths be less than 100? Modeling Functions - Regression Project Write Up Year Population 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2033 2031 2032 2034 2035 2036 Equation y= 530000 (1-.25) x * y= 530000 (.75) x * 2042 530000
397500
298125
223574
167694
125772
94329
76747
53059
39795
29847
22385
16789
12592
9444
7083
5312
3984
2988
2241
1681
1260
946
709
532
95 Interpolation As you will see below, I used my equation:
y= 530000 * (.75)^x and did the process. 530000= initial number of deaths....
multiplied by....
the rate which is .75 (25%). It is a number less than 0, because crime rate is decreasing each year. (Exponential decay).
Once you do that you have to do your exponential power which is, x.
# of years Regression a= 711826.9942
b= 75 The Graph Analysis As we can see by the graph to the left, it is exponential decay. Instead of the graph exponentially rising, it decays and this is exactly what we want to happen. According to the problem crime rate decreases exponentially and we see that here. The line of best fit is shown in red as well as the points in green. Extrapolation One of the questions asked; when would the number of deaths be less than 100. Using the equation, I plugged in different year dates after 25 years. I got that after 30 years there will only be 95 deaths.
Hopefully after 43 years, there will be nearly no crime at all in Detroit because as statistics show, by year 43, there will be 3 deaths and after that, crime rate will disappear. http://www.walterzorn.de/en/grapher/grapher_e.htm

ttp://www.huffingtonpost.com/2012/11/30/detroit-2012-murders-homicides-murder_n_2218233.html

Sites I chose this project because I was sitting and thinking of a good exponential problem. Population exponential is very popular. So then I thought of a situation and because there has been so much death lately after the Conn. incident, I chose crime rate in Detroit. Any kind of death is hard to deal with and if it were possible to rid so much crime, it would be good for society all over the world. I chose Detroit because it is one of the largest cities where crime occurs everyday. I picked a random number of deaths which does create a fault in my project just because my numbers are not logistic to the real world. This would all represent exponential decay. I know that through the 2nd amendment, we have the right to bear arms but there should be restrictions because it's immoral to go around killing people.
I had to experiment with different data so that I would end up with a reasonable data set. I first had that crime rate decrease by 15% but thought it was too large of a number. I was incorrect because then i lowered it to 10% then to 2%. Those were way too low and over the 25 year period, it would not drop below 30,000. So I raised it all the way to 25% and this was a good rate. Hypothetically, this would be a really good situation because if crime rate in Detroit did decrease because they restricted the right bear arms, then not so many people would be going around with guns killing each other. So yes, hypothetically this is a real world situation. Plus it would all happen within in a 43 year period which is amazingly fast.
Say that crime rate all over the world was increasing and they found out that it was because of people just buying fire arms because there was no restriction as to who can attain a permit. Well, maybe limiting the rules for attaining a fire arm permit would decrease the number of crime rate because now not everyone has one just because they wanted one. If less people own firearms, then the less likely it is for someone to go around who has bad motifs because they were not able to get a gun.
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