Abstract
This paper is dedicated to the importance of mathematical models and their application to the solution of real world problems. The purpose of this paper is to demonstrate how the relationship between two variables or factors can be mathematically expressed. I selected the following variables: the unemployment rate and violent crime rate of the United States of America. The three points selected are the unemployment and violent crime rate in 1998-2000. The linear equation was created on the basis of two points in 1998 and 2000. He equation shows that there is a positive relationship between the number of violent crimes and the unemployment rate. This equation was used to estimate the violent crime rate of the U.S. in 1999. The obtained value of 530.94 is not significantly different from the actual value of 523.0. This equation can be used in forecasts and approximations. I conclude that the mathematical model is useful and reliable tool to deal with the real world problems.
Unemployment Rate and Crime Rate
Mathematics is a great tool to model a real world problems in the terms of measurable indicators or variables. In this paper, I will demonstrate how mathematics can be applied to a real world problem. I collect the information about the unemployment and violent crime rates in the United States of America and create a mathematical model to represent the relationship between these rates.
The unemployment rate data are retrieved from Statistica, the statistical portal ("Unemployment rate in the U.S. 1990-2015 | Timeline", 2016). According to this data, the unemployment rates in 1998-2000 were as shown in the table below:
The violent crime rate for the considered period is taken from the Uniform Crime Reporting Statistics website ("Uniform Crime Reporting Statistics", 2016). The data are represented in the table below:
Thus, the summary data can be represented as follows:
Now I am able to create an equation that fits the two points – I select 1998 and 2000 year as these two points. First, find the slope of the linear equation:
m=y2-y1x2-x1=506.5-567.64-4.5=-61.1-0.5=122.2
The slope is equal to 122.2.
Now, write the equation in the point-slope form:
y-y1=mx-x1y-567.6=122.2x-4.5y-567.6=122.2x-549.9y=122.2x+17.7
Here, y represents the number of violent crimes per 100,000 population, x is the unemployment rate, in %. The 567.6 represents the initial violent crime rate in 1998. The 506.5 is the value of violent crime rate in the end of the period – 2000. The initial unemployment rate was 4.5% (in 1998). The unemployment rate if 2000 is 4.0%. I want to estimate the violent crime rate in 1999 by using this linear equation:
y=122.2*4.2+17.7=530.94
According to the forecast, the violent crime rate in 1999 is 530.94 per 100,000 population. The actual value is 523.0. It is possible to visualize the line and the points in the graph below:
References
Unemployment rate in the U.S. 1990-2015 | Timeline. (2016). Statista. Retrieved 14 August 2016, from http://www.statista.com/statistics/193290/unemployment-rate-in-the-usa-since-1990/
Uniform Crime Reporting Statistics. (2016). Ucrdatatool.gov. Retrieved 14 August 2016, from http://www.ucrdatatool.gov/
