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7/30/2019 Crime in States
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Statistical analysis of the
relation between Crime Rate,Education and Poverty: USA,
2009
Sonarika Mahajan
100076
7/30/2019 Crime in States
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Research Question
In this research paper, analysis is done to conclude whether the level of education and
poverty influence the total crime rate in the United States of America. Using descriptive
statistics such a mean, standard deviation, variance, histograms, scatter diagrams and simple
linear regression analysis performed upon both independent variables separately, it can be
analysed till what extent do these two independent variables, i.e. education and poverty cause
fluctuations upon the dependent variable, in what proportion (direct or inverse) and of the
two independent variables, which is a better predictor for determining crime rate in USA.
Data description
[The states selected for this study are highlighted with yellow in the above map]
The Data that is used to define our dependent variable include both, violent crime (murder
and non- negligent manslaughter, forcible rape, robbery, and aggravated assault) as well as
property crime (burglary, larceny-theft, motor vehicle theft, and arson). Crime statistics used
in this study are published by FBI (Federal Bureau of Intelligence) serving as a governmental
agency to the United States Department of Justice.
The independent variable that comments upon the education levels in the United States of
America is carried out by analysing the total number of public high school graduates per
state. This data includes students of all the ethnicities for the school year 2008-2009. The
education universe in this study is equivalent to the total population of the state. This data has
been collected by National Centre for Education Statistics (NCES), which is the primary
federal entity that collects education related data in the U.S. and other countries and analyses
it.
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The poverty status for an individual is measured by comparing his/her income to a preset
amount of dollars known as the threshold value. The poverty universe excludes children
below the age of 15, people living in military barracks, institutional group quarters and
college dormitories. This data is collected by the U.S. Census Bureau, serving as the most
reliable source about Americas people and economy.
All the data collected is cross-sectional, since it was taken during the same time period (year
2009) across different parameters. Also, the scale of measurement for these variables is the
ratio scale, since the ratio between two values is meaningful and the observations are
comparable to a zero value.
Analysis
Mean: It is the representative of a central value for a given data set, i.e. average.
The mean value for crime variable suggests that in the year 2009, the percentage of crimes
being reported in any state of USA was 3.26%.
The mean value for education variable suggests that the percentage of public high school
graduates being reported in any state of USA was 1% for the same time period.
Similarly, the mean value for the poverty variable suggests that the percentage of individuals
living below the poverty line being reported in any state of USA was 13.54%.
Standard deviation & Variance: The higher the value of the standard deviation, greater is the
dispersion of the data set. Out of the three variables, poverty has the highest standard
deviation value of 2.98. Therefore, the percentage of individuals below poverty level is more
widely dispersed over the states as compared to the other two variables.
Variance is the average of the sum of squared deviation scores. It is used to compute the
standard variation since its a better means for determining the dispersion of data. It is
measured as the square of standard deviation for any data set.
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Skewness: The symmetry of the variable distribution is measured by the help of this statistic.
Crime rate has a skewness of 0.083, making it a symmetrical distributed variable since the
value is closer to zero.
The education variable is skewed negatively at -.367 since the variable has lower values,
indicating a left skewed histogram.
Whereas, poverty shows a positive skewness value of .670 since its variables have numerous
high values, which justifies the right skewness of the histogram.
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Simple linear regression model:
a. Crime and Education -
Y = Dependent variable, CrimeX = Independent variable, Education.
The regression model is the equation that describes how y is related to x.
This regression equation is:
From Table 2.4 in appendix, the regression equation is,
Crime = 6.17 - 2.9 (Education)
This regression equation can be graphed as follows assuming 0as the intercept and 1 as the
slope:
Interpretation of the slope: For every 1% increase in the number of students being graduated
from high school, there is a decrease of 2.9% in crime activities in the USA.
Interpretation of the intercept: Even if there is no variation in the education level, the
estimated crime rate would be 6.17%.
The coefficient of determination or r2: It determines the proportion of variation in the
dependent variable by the independent variable.
From Table 2.2, r2
= .181
This states that 18.1% of the variation in crime rate is explained by regression of education
on crime. Since this value is not close to 1, it doesnt seem to be a appropriate predictortodetermine the crime rate in USA.
Here the slope 1
is negative.
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Hypothesis testing:
Ho: 1 = 0 (education is not a useful predictor of crime)
Ha: 1 0 (education is a useful predictor of crime)
Significance level: = 0.05
According to the rejection rule, the null hypothesis will be rejected if p-value .
From table 2.4, p-value = 0.019
Since 0.019 0.05, we reject the null hypothesis.
At 95% confidence level, there is enough evidence to conclude that education is a useful
predictor for crime in USA since the slope of the regression line is not zero.
b. Crime and Poverty:
Y = Dependent variable, Crime
X = Independent variable, Poverty.
The regression equation is as follows:
Plugging in the values to from Table 3.4, get:Crime = 1.819 + 0.107 (Poverty)
This regression equation can be graphed as follows assuming 0 as the intercept and 1 as the
slope:
Here the slope 1
is positive.
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Interpretation of the slope: For every 1% increase in the individuals below poverty line, there
is an increase of .11% in crime activities in the USA.
Interpretation of the intercept: With the poverty level remaining constant, the estimated crime
rate would be 1.82%.
The coefficient of determination or r2
From Table 3.2, r2
= .191
This states that 19.1% of the variation in crime rate is explained by regression of poverty on
crime.
Hypothesis testing:
Ho: 1 = 0 (poverty is not a useful predictor of crime)
Ha: 1 0 (poverty is a useful predictor of crime)
Significance level: = 0.05
According to the rejection rule, the null hypothesis will be rejected if p-value .From table 3.4, p-value = 0.016
Since 0.016 0.05, we reject the null hypothesis.
At 95% confidence level, there is enough evidence to conclude that poverty is a useful
predictor for crime in USA since the slope of the regression line is not zero.
Conclusion and recommendations
From this study conducted, it is assured that the crime rate in USA is directly proportionate to
the people below the poverty line and inversely proportionate to the number of high school
students graduating in the year 2009. When simple linear regression was performed to both
the independent variables separately, the coefficient of determination (r2) and the p-value
aided our study to select the variable that was a better predictor for determining the crime rate
in America. Poverty, with the significance level of 19.1% is known to be a better predictor in
this case as compared to the 18.1% significance level shown by the independent variable,
education. This fact was further proved when the p-value for poverty stood at a lower
amount as compared to its counterpart.
Even though it can be concluded that poverty is a better predictor for crime rate in USA, thelevel of significance still stands at a diminutive 19.1%. Much stronger predictors could be
used for the above study. GDP, income level, provision of federal aid or employment rate
could be a few options to choose amongst.
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Appendix
Table 1.1 Statistics for crimes reported in 30 states of USA.
State Population ViolentCrime PropertyCrime Total CrimePercentage ofTotal Crime
Alabama 47,08,708 21,179 1,77,629 1,98,808 4.22
Alaska 6,98,473 4,421 20,577 24,998 3.58
Arizona 65,95,778 26,929 2,34,582 2,61,511 3.96
California 3,69,61,664 1,74,459 10,09,614 11,84,073 3.20
Colorado 50,24,748 16,976 1,33,968 1,50,944 3.00
Connecticut 35,18,288 10,508 82,181 92,689 2.63
Florida 1,85,37,969 1,13,541 7,12,010 8,25,551 4.45Hawaii 12,95,178 3,559 47,419 50,978 3.94
Iowa 30,07,856 8,397 69,441 77,838 2.59
Kansas 28,18,747 11,278 90,420 1,01,698 3.61
Michigan 99,69,727 49,547 2,82,918 3,32,465 3.33
Minnesota 52,66,214 12,842 1,39,083 1,51,925 2.88
Mississippi 29,51,996 8,304 87,181 95,485 3.23
Missouri 59,87,580 29,444 2,02,698 2,32,142 3.88
Montana 9,74,989 2,473 24,024 26,497 2.72
Nebraska 17,96,619 5,059 49,614 54,673 3.04
Nevada 26,43,085 18,559 80,763 99,322 3.76
New Jersey 87,07,739 27,121 1,81,097 2,08,218 2.39
New Mexico 20,09,671 12,440 75,078 87,518 4.35
New York 1,95,41,453 75,176 3,78,315 4,53,491 2.32
North
Carolina
93,80,884 37,929 3,44,098 3,82,027 4.07
North
Dakota
6,46,844 1,298 12,502 13,800 2.13
Oregon 38,25,657 9,744 1,13,511 1,23,255 3.22
Pennsylvania1,26,04,767 47,965 2,77,512 3,25,477 2.58
South
Dakota
8,12,383 1,508 13,968 15,476 1.91
Texas 2,47,82,302 1,21,668 9,95,145 11,16,813 4.51
Virginia 78,82,590 17,879 1,91,453 2,09,332 2.66
Washington 66,64,195 22,056 2,44,368 2,66,424 4.00
Wisconsin 56,54,774 14,533 1,47,486 1,62,019 2.87
Wyoming 5,44,270 1,242 14,354 15,596 2.87
Source:http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-5
http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-5http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-5http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-5http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-57/30/2019 Crime in States
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Table 1.2 Statistics for public high school graduates in 30 states of USA.
State Population Total Public
High
School
Graduates
Percentage of
High School
Graduates
Alabama 47,08,708 42,082 0.89
Alaska 6,98,473 8,008 1.15
Arizona 65,95,778 62,374 0.95
California 3,69,61,664 3,72,310 1.01
Colorado 50,24,748 47,459 0.94
Connecticut 35,18,288 34,968 0.99
Florida 1,85,37,969 1,53,461 0.83
Hawaii 12,95,178 11,508 0.89
Iowa 30,07,856 33,926 1.13
Kansas 28,18,747 30,368 1.08
Michigan 99,69,727 1,12,742 1.13
Minnesota 52,66,214 59,729 1.13
Mississippi 29,51,996 24,505 0.83
Missouri 59,87,580 62,969 1.05
Montana 9,74,989 10,077 1.03
Nebraska 17,96,619 19,501 1.09
Nevada 26,43,085 19,904 0.75
New Jersey 87,07,739 95,085 1.09
New Mexico 20,09,671 17,931 0.89New York 1,95,41,453 1,80,917 0.93
North
Carolina
93,80,884 86,712 0.92
North
Dakota
6,46,844 7,232 1.12
Oregon 38,25,657 35,138 0.92
Pennsylvania 1,26,04,767 1,30,658 1.04
South
Dakota
8,12,383 8,123 1.00
Texas 2,47,82,302 2,64,275 1.07
Virginia 78,82,590 79,651 1.01
Washington 66,64,195 62,764 0.94
Wisconsin 56,54,774 65,410 1.16
Wyoming 5,44,270 5,493 1.01
Source:http://nces.ed.gov/CCD/tables/ESSIN_Task5_f2.asp
http://nces.ed.gov/CCD/tables/ESSIN_Task5_f2.asphttp://nces.ed.gov/CCD/tables/ESSIN_Task5_f2.asphttp://nces.ed.gov/CCD/tables/ESSIN_Task5_f2.asphttp://nces.ed.gov/CCD/tables/ESSIN_Task5_f2.asp7/30/2019 Crime in States
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Table 1.3 Statistics for individuals below Poverty line in 30 states of USA.
State Population for
whom poverty
status isdetermined
Individuals
in poverty
Percent
below
poverty
Alabama 45,88,899 8,04,683 17.54
Alaska 6,82,412 61,653 9.03
Arizona 64,75,485 10,69,897 16.52
California 3,62,02,780 51,28,708 14.17
Colorado 49,17,061 6,34,387 12.90
Connecticut 34,09,901 3,20,554 9.40
Florida 1,81,24,789 27,07,925 14.94
Hawaii 12,64,202 1,31,007 10.36
Iowa 29,05,436 3,42,934 11.80
Kansas 27,32,685 3,65,033 13.36
Michigan 97,35,741 15,76,704 16.20
Minnesota 51,33,038 5,63,006 10.97
Mississippi 28,48,335 6,24,360 21.92
Missouri 58,18,541 8,49,009 14.59
Montana 9,46,333 1,43,028 15.11
Nebraska 17,39,311 2,14,765 12.35
Nevada 26,06,479 3,21,940 12.35New Jersey 85,31,160 7,99,099 9.37
New Mexico 19,68,078 3,53,594 17.97
New York 1,90,14,215 26,91,757 14.16
North Carolina 90,95,948 14,78,214 16.25
North Dakota 6,20,821 72,342 11.65
Oregon 37,48,545 5,34,594 14.26
Pennsylvania 1,21,65,877 15,16,705 12.47
South Dakota 7,82,725 1,11,305 14.22
Texas 2,41,76,222 41,50,242 17.17
Virginia 76,23,736 8,02,578 10.53
Washington 65,30,664 8,04,237 12.31
Wisconsin 54,95,845 6,83,408 12.43
Wyoming 5,29,982 52,144 9.84
Source:
http://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth/income_and
_poverty--state_and_local_data.html
http://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth/income_and_poverty--state_and_local_data.htmlhttp://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth/income_and_poverty--state_and_local_data.htmlhttp://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth/income_and_poverty--state_and_local_data.htmlhttp://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth/income_and_poverty--state_and_local_data.htmlhttp://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth/income_and_poverty--state_and_local_data.html7/30/2019 Crime in States
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Regression (Independent variable: Education)
Table 2.1
Variables Entered/Removedb
Model
Variables
Entered
Variables
Removed Method
1 Educationa
. Enter
a. All requested variables entered.
b. Dependent Variable: Crime
Table 2.2
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .425a
.181 .152 .67068
a. Predictors: (Constant), Education
Table 2.3
ANOVAb
Model Sum of Squares df Mean Square F Sig.
1 Regression 2.784 1 2.784 6.189 .019a
Residual 12.595 28 .450
Total 15.379 29
a. Predictors: (Constant), Education
b. Dependent Variable: Crime
Table 2.4
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig.B Std. Error Beta
1 (Constant) 6.165 1.173 5.257 .000
Education -2.904 1.167 -.425 -2.488 .019
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Regression (Independent variable: Poverty)
Table 3.1
Variables Entered/Removed
b
Model
Variables
Entered
Variables
Removed Method
1 Povertya
. Enter
a. All requested variables entered.
b. Dependent Variable: Crime
Table 3.2
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .437a
.191 .162 .66665
a. Predictors: (Constant), Poverty
Table 3.3
ANOVAb
Model Sum of Squares df Mean Square F Sig.
1 Regression 2.935 1 2.935 6.604 .016a
Residual 12.444 28 .444
Total 15.379 29
a. Predictors: (Constant), Poverty
b. Dependent Variable: Crime
Table 3.4
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig.B Std. Error Beta
1 (Constant) 1.819 .575 3.162 .004
Poverty .107 .042 .437 2.570 .016
a. Dependent Variable: Crime
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