Impact of Educational Attainment on Crime
in the United States:
A Cross-Metropolitan Analysis
Georgia Institute of Technology
ECON 3161, Econometric Analysis
Brian Gentry, Rishab Mokkapati & Kiran Rampersad
November 17, 2016
Abstract:
This study seeks to find a relationship between educational attainment of the population aged
18 years and older, and violent and property crime, in 342 metropolitan areas across the United
States. While past studies have researched this relation, they have not done so on a metropolitan
scale . Regression models were formed using 2015 data obtained from both the US Census Bureau
and the Federal Bureau of Investigation (FBI) . The simple linear regression model found a negative
relationship between educational attainment and crime. The more educated a metropolitan
population is, the lower its crime levels. Multiple linear regression analyses found that this
correlation holds even as other variables are added to the regression. Although this negative
correlation is weak, it is still statistically significant.
1. Introduction
Throughout recent history, educational attainment has garnered great attention in the
American government’s agenda. The Bush administration pumped billions of dollars into the No Child
Left Behind program while the Obama administration invested billions in ventures such as Race to the
Top and Education Jobs Fund. Education is seen as a tool for social improvement, uplifting the poor
and changing lives. However, it also has been seen to have an impact upon crime rates. Many of those
who turn to crime are stereotyped as uneducated and desperate. Although the stereotype might be
false, the underlying principle is thought to be true; increased educational attainment may have a
negative correlation upon crime rates. By gaining some level of education, one can find employment
and not have to resort to crime.
There have been numerous studies done on the impact of education on crime. Education is
generally regarded as a human capital investment that increases work opportunities in the future and
thus discourages participation in crime. Moreover, human capital raises the marginal returns from
work more than crime which discourage criminal activity (Lochner, 2011). Groot and van den Brink
(2010) argue that educational attainment reduces crime levels because it increases the opportunity
costs from forgone earnings and expected costs of incarceration. Fella and Gallipoli (2014) in their
theoretical study, concluded that a subsidy to high school completion provides large welfare gains and
subsequently reduces crime. Thus, by investing in education, the population is more skilled and
knowledgeable, and substantial savings on the social costs of crime can be attained.
While there exists an abundance of literature on the association between educational
attainment and crime, the relationship between these two variable at the metropolitan level has not
been extensively researched. Metropolitan cities are on the rise as they are emerging faster and
larger. The goal of this paper is to uncover the empirical relationship between educational attainment
and crime levels across 342 metropolitan statistical areas (MSAs) across the United States, using
regression analysis. The model developed in this study will seek to find a correlation between
educational attainment of individuals who are above the age of 18 and crime levels ( violent and
property crimes) using metropolitan-specific data obtained for 2015.
2. Literature Review
Other studies linking education with crime show that there is a correlation between the
amount of education an individual has and the amount of crime they are predicted to commit. In
2011, Lance Lochner analyzed the relationship between the number of years of schooling individuals
had and the number of times they went to and the years they spent in prison. Lochner (2011)
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hypothesizes that additional schooling, namely years spent increasing human capital in close
proximity to others, lowers the returns on crime relative to the returns on work, and expresses this in
terms of dollars per year. He also notes that better schools tend to reduce delinquency rates and later
felony conviction rates: students from low income families more disposed to crime who had been
placed in high performing schools via lottery showed a 45% reduction in felony convictions
comparative to their peers up to seven years afterwards. After the forced desegregation in of schools
in the American South, many low income African American families were able to send their children to
better funded schools. This led to a 17% drop in homicides among African Americans of high school
age. This in turn suggests that better school quality, as Lochner states, is more effective in deterring
crime. However, his method measures the conviction rates of crime, not necessarily the actual crime
statistics of the students he studies.
Fella and Gallipoli’s (2014) comparative study offers significant insight as to the relative
magnitude of increased spending on education upon crime. Fella and Gallipoli (2014) do measure the
impact of increasing enrollment rates upon the crime rate, and then correlate the enrollment rates to
graduation subsidies. The paper definitively shows that increasing the enrollment numbers decreases
the amount of crime at a given time, by giving individuals necessary tools to enter the workforce
instead of turning to crime. However, their model seeks to keep students who would otherwise drop
out of school to work or commit crime by paying them a subsidy, rather than investing in
improvements to the schools themselves. The study does not take into account the achievement rates
of the individuals in the schools, and therefore shows the impact of merely keeping students in school
longer, rather than improving the quality of their education or improving the school systems to
motivate students.
Groot and van de Brink (2010) is similar to Lochner’s model in terms of the design of their
analysis. Focusing on the relative amount of education each individual has and comparing it to their
crime statistics later in life, van de Brink maps out the effects of an additional year of education on
individuals, and finds that additional years of education decrease tendencies to commit violent crime,
breaking and entering, and tax fraud. However this has little to no noticeable effect upon petty crime
statistics. By focusing on years of schooling, Groot and van de Brink (2010) try to map out the quantity
of schooling a person has comparatively to their predisposition to commit crimes. Their analysis
shows that an additional year’s schooling tends to result in less perpetration of vandalism, petty theft,
and other minor crimes, resulting in massive savings in government expenditure in crime prevention
and social welfare. However, their study doesn’t address the quality of schooling addressed in
Lochner’s analysis, a key component in our observations. While learning about how increasing the
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amount of time spent in the classroom would certainly be useful, without evaluation on how much
personal capital the students gained, the impact of how the schooling actually improved their
potential to the point at which crime became unprofitable.
Marlow (2001) writes about the correlational fallacy between education and crime prevention
expenditure. By looking at the various factors which might contribute to increased education or crime
prevention expenditure (including political party at the head of local government, diversity of local
community, and the average education level of the local community) he charts the relative impact an
increase in education expenditure might have on expenditures in crime prevention. The study finds
that there is little to no correlation between the two forms of expenditure, meaning that increased
educational spending doesn’t result in a decrease of the amount spent to control crime. This is useful
to us because it indicates we don’t need to control for crime expenditure in building our multiple
regression model; but the study itself doesn’t track the effects of the expenditure on education on the
crime level at all.
Mark Anderson’s (2014) study gives additional credibility to the idea that schooling itself plays
a role in keeping juvenile crime rates low. By analyzing the impact of changes in the Minimum
Dropout Age (MDA), Anderson found that increased MDA reduced the number of juveniles of the age
the MDA now covered by nearly 10 percent. In addition, a movement across the United States to
increase the minimum dropout age to 18 would theoretically decrease the juvenile crime rate by 17
percent. This drop could be contributed to the idea that students in school have less incentive or time
to go looking fro crimes to commit. Although the study demonstrates a negative correlation between
education attendance and crime rates, the study is specifically focused on juvenile crime rates,
whereas our study will be covering violent and property crime rates for adults i.e. 18 years and older.
Our research will avoid focusing on the broad picture or the simple amount of schooling
received by students, by focusing on such attainment at the metropolitan level. This differs from
previous studies in the sense that we will not be looking at the data surrounding individualsindividual grades and individual crime statistics. Instead of only tracking the number of individuals in
schools, we will be looking at the level of the education they received, thereby focusing on their
educational attainment as opposed to the enrollment rates. Our study hopes to discover whether an
increased educational attainment deters crime more later in life- not whether keeping individuals off
the street in their youth prevents crime.
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3. Data
3.1 Variables
The purpose of this study was to determine the causal relationship between educational
attainment and the crime level in 342 randomly selected metropolitan cities across the United States.
(Breakdown on region found in table 2) Crime levels were measured with violent and property crime
values obtained for each of these metropolitan cities. Violent crimes include rape, murder and
manslaughter, robbery, aggravated assault. Property crimes include burglary, larceny-theft, and
motor vehicle theft. To measure the level of educational attainment, the number of individuals 18 and
older who reported graduating high school was used.
High school graduation was used, as opposed to other degrees for two reasons. The major
reason why high school graduation rates were used over any other degrees (or non-degrees) in the
explanation of property crime is the considerable increase in employment opportunities between high
school graduates and non-graduates. Although these employment opportunities do not provide
comparable financial support to those opportunities available to bachelors and masters degree
holders, it is sufficient to provide a living. For those who did not graduate high school there are
considerably fewer jobs available, and thus they are more likely to be driven to property crime to
obtain financial support. In terms of violent crime, the high school diploma represents an individual’s
completion of four years of interacting with other individuals and the initial determination of their
identity. Due to their interactions with other high school students and teachers, and their instruction
in the social studies, former high school students are more equipped to control their emotions and
find legal, and appropriate means of conveying their emotions.
In order to ensure that the results from this study accounted for population, the overall
population of each of these metropolitan per 100,000 people was used to determine the amount of
crime, violent and property, and the percentage of the population, 18 years and older, who have
graduated from at least high school and received a high school diploma, was used to measure
educational attainment.
We used seven different variables to explain crime rates in each metropolitan area. Table 1
shows the description of the variables used in the simple linear regression model. Education, if used
to try to solely explain crime rates, faces a serious omitted variable bias; a high school education alone
is unlikely to deter someone from crime. The addition of other explanatory variables was necessary to
cover other factors towards crime.
5
Unemployment (unemploy) represents the percent of the population which reported itself as
unemployed in 2015 for each metropolitan area. We expected a positive correlation between
Unemployment and crime- as more individuals in an area are employed, they have less reason to
commit violent or property crimes as the opportunity costs from incarceration rise. Median age was
also accounted for in our analysis since the age plays a factor in determining if an individual commits
property or violent crime. We expect a negative correlation between crime levels and median age in
the metropolitan area due to the tendency of younger individuals to be the perpetrators of violent
and property crime. We expect a positive relationship between Gini levels and crime- the higher the
income disparity, the more temptation for those in poverty to engage in criminal activity. Finally,
poverty was included and expected to have a positive correlation on crime since those in poverty have
a greater incentive to try to improve their lives through crime.
Table 1: Variable Descriptions
Variable
Description
crime
Crime level per 100,000 of population (18 years and older)
educ
Percentage of population who graduated from high school (18 years and older)
age
Median age of entire population
unemploy
Unemployment rate of workforce
gini
Gini coefficient - Income distribution of population (measure of inequality)
poverty
Percentage of people who earned an income under poverty level
Table 2: Geographical Distribution of Metropolitan Statistical Areas
US Region
Number of Metropolitan Statistical Areas
Northeast
51
Midwest
71
Southeast
105
Southwest
38
West
77
Total
342
6
3.2 Sources
All of the education data was obtained through the American Fact Finder based on US Census
Bureau data through the American Community Survey (ACS). The survey provides vital information
about the United States and its people. The survey yielded information regarding the number of
people who received a high school degree or higher among an 18 or older population in metropolitan
cities around the nation. The additional variables that were added for use in the multiple regression
analysis were obtained through the US Census Bureau’s American FactFinder database. The crime
data and the population information for metropolitan cities was obtained through the Federal Bureau
of Investigation’s Uniform Crime Reporting (UCR) database. The UCR provides crime data for 18,000
cities, university/college, county, state, tribal, and federal law enforcement agencies voluntarily
participating in the program. All data collected was from 2015.
3.3 Summary Statistics
Table 3 shows the summary statistics of the six variables used in our regression models.
Table 3: Summary Statistics
Variable
Observations
Mean
Standard Deviation
Minimum
Maximum
crime
342
3808.89
1299.05
211.46
7692.20
educ
342
87.67
5.05
64.96
98.78
age
342
38.07
4.98
24.60
66.50
unemploy
342
6.31
2.05
2.3
16.5
gini
342
0.46
0.03
0.39
0.54
poverty
342
15.65
4.34
6.62
32.43
3.4 Gauss Markov Assumptions
The first assumption states that the model should be linear in parameters. Since the models
used in our regression analyses are written in the form of Y = β0 + β1 X
1 + β2 X
2 +.…..+ βk X
k + u,
assumption 1 is satisfied. For the second assumption, there should be random sampling of regressors.
The 342 metropolitan statistical areas used in our regression analysis were randomly selected from a
7
total of 374. The third assumption states that there should exist no perfect collinearity between any
of the independent variables. Table 4 shows that no two independent variables are perfectly
positively or negatively correlated. Since there are no exact linear relationships between the
regressors, assumption 3 is satisfied.
Table 4: Correlation Between Variables
crime
educ
age
-
unemploy
gini
crime
1
educ
-0.35
1
age
-0.23
0.13
1
unemploy
0.30
-0.40
0.04
1
gini
0.20
-0.17
-0.05
0.17
1
poverty
0.42
-0.52
-0.28
0.49
0.45
poverty
-
-
-
-
-
-
-
-
-
-
-
-
1
The fourth assumption states that the error term, u, should have an expected value of zero
given any value of the independent variables. The summary statistics of the residuals from MLR2 is
shown in Table 5 below. Since the mean of the residuals was found to be 4.35e-07, which is
approximately zero, assumption 4 is met.
Table 5: Summary Statistics for Residuals in MLR2
resid
Observations
Mean
Standard Deviation
Minimum
Maximum
342
4.35e-07
1143.39
-3352.91
3460.77
The fifth and final assumption requires the error term, u, to have a constant variance given
any value of the explanatory variables. The residual distribution in Figure 1 demonstrates a normal
curve. Thus, assumption 5 is met.
8
Figure 1: PDF of Residuals
Note: This is the pdf of the residual from regressing crime on educ, age, unemploy, gini and poverty.
4. Results
4.1 Simple Linear Regression
In the simple regression model, crime was the dependent variable and educational attainment
was the independent variable, as seen in Equation 1 below. Our model gave a negative relationship
between crime and educational attainment (educ) as shown in the scatter plot in Figure 2. For each
additional one percent of the population who graduates from high school, the linear regression shows
that there is a decrease of 89.1 violent and property crimes per 100 thousand people within each
metropolitan area. Although this negative correlation supports our hypothesis, it only does so very
loosely- the r-squared value of the simple linear regression is only 11.98 percent. This is due to the
omitted variable bias- although education has a negative relationship with crime, lack of education is
not enough to explain crime statistics (see table 6).
SLR Model: crime = β0 + β1 educ
+ u
9
Figure 2: Scatter Plot of Crime Level (per 100,000 people) versus
Persons Graduating From High School (%)
Note: Both crime level and persons graduating from high school were measured for the population, 18
years and older. Two outliers were removed from the original data set.
4.2 Multiple Linear Regression
As discussed earlier, simply regressing education and crime will not show the true effects
education has on crime due to the omitted variable bias. In order to rectify this discrepancy, several
other variables were added in order to create a better relationship, and multiple regression analysis
was performed.
The first multiple linear regression model includes the explanatory variables age (age) and
unemployment rates (unemploy). These were selected because an aging median population should
reduce the amount of individuals fit enough to engage in violent or property crimes. With the
10
reduction of the omitted variable bias placed upon educ, the number of major crimes reduced by an
increase in educated population decreases to 60.42, but the other variables show increased impact
upon the crime rates: for each year older the median population is in each metropolitan area, crime
rates fall by 52.88 per 100k, and for each additional percent unemploy increases, the amount of crime
increases by 132.63. The r-squared value has increased significantly, to 18.88 percent. The addition of
the new explanatory variables still does not control for all of the reasons behind crime, but each of
the individual variables have added additional validity to the model. (See table 6)
MLR1 Model: crime = β0 + β1 educ
+ β2 age
+ β3 unemploy
+ u
The second and final multiple linear regression model adds the gini coefficient (gini) and the
poverty rate (poverty) of each metropolitan area to the model. This in turn increases the r-squared
value to 22.53 percent, but lead to much decreased impact of each of the original variables. Educ still
reduces violent crimes per 100k by 40.14 per percent increase, each additional year added to the
population median still decreases crime rates by 38, and each additional percent of the population
unemployed increases the number of crimes by 77.82. Gini has an extremely strong positive
correlation; as the gini coefficient increases from 0 to 1, we see an increase in property and violent
crimes by 2434.6. Poverty likewise shows a positive correlation; for each percent the poverty rate
increases, the number of crimes increases by 65.25. However, the significance of the variables can be
called into question, as will be discussed later on (see table 6).
One of the aspects which we find most significant about all our data sets is the relatively high
level of our intercept. Although it drops significantly between our second and third model, the
intercept starts at 11621 in our SLR, drops to 10282 in our first MLR, and drops further to 6152 in our
second and final MLR. This is indicative, perhaps, of a baseline level of crime that occurs in any
economy.
MLR2 Model: crime = β0 + β1 educ
+ β2 age
+ β3 unemploy
+ β4 gini
+ β5 poverty
+ u
11
Table 6: OLS Regression Estimates
Dependent Variable: crime
Independent
Variables
educ
SLR Model
MLR1 Model
MLR2 Model
-89.111
(0.000)***
-60.417
(0.000)***
-40.139
(0.007)***
age
-
-52.886
(0.000)***
-37.996
(0.005)***
unemploy
-
132.631
(0.000)***
77.823
(0.035)**
gini
-
-
2434.609
(0.362)
poverty
-
-
65.251
(0.002)***
Intercept
11621.07
(0.000)***
10282.64
(0.000)***
6152.061
(0.001)***
No. of Observations
342
342
342
R-Squared
0.1198
0.1888
0.2253
Significance Level Key: *10%, **5%, ***1% level
Note: Values in parenthesis are the respective p-values for each variable.
4.3 Statistical Inferences
The first two models are straightforward when it comes to significance; all of the variables
have t-values which places them as significance at all of the three standard levels of significance. In
the first model, this data is very misleading; the high t-values mask the fact that there is significant
omitted variable bias, leading to overdependence on education, which contributes to the low
r-squared value of the model. The second model is much better; with additional variables, the
pressure on educ to explain crime in its entirety is reduced, while each of the variables is still
significant at every significance level. The low overall r-squared value is likely because no one variable
can account for every crime, and we can barely scratch the surface of the number of reasons to
commit one.
12
The final model, which included gini and poverty, has several disconcerting changes. Although
in previous models all of the variables were significant, gini and unemployment are no longer
significant at the 1%, and gini is not significant at any of the standard significance levels, with a
p-value of only 0.91. Gini is an interesting statistic, as it is graded on a scale of 0 to 1, and wit its
relatively low variance of 0.15, small changes can seem to have massive impacts, as we can see from
its correlation, However, its lack of significance level is telling- even at the 10% level, it fails to be
significant. This shows that income inequality may be correlated with higher crime rates, but is
unlikely to explain it. Unemployment, however, has only seen a slight decrease in its effectiveness,
and is now only significant at the 10% and 5% values. This may be because of moderate levels of
colinearity between poverty and unemploy. As unemploy increased, poverty does as well, as we see in
table 4 above. Poverty itself, interestingly enough, is significant at all three primary significance levels.
One of the promising impacts of the final model is that all of the variables save gini have significant t
values- but none have excessive t-values. We surmise that this indicates that the final model manages
to avoid completely the omitted variable bias, which plagued educ in the earlier models. Thus, the
third model is the most representative of the impact of each variable on crime.
4.4 Robustness
We conducted several F-tests and partial F-tests to determine the usefulness of our models.
Table 7 below contains all the results from these robustness tests. First, the SLR model was found to
be useful as a whole. Next, we tested our MLR1 model, where we added the variables age and
unemploy. The MLR1 model was also useful as a whole. From the partial F-test on MLR1, age and
unemploy proved to be jointly significant indicating that the entire unrestricted model (MLR1) should
be chosen. Lastly, we tested our MLR2 model, where we added the variables gini and poverty. This
model was useful as a whole. However, gini is insignificant at all levels, and unemploy loses
significance at the 1% level. The partial F-test on MLR2, proves that although gini and unemploy loses
some significance individually, they are jointly significant with the other additional independent
variables educ, age and poverty. Thus, the unrestricted model (MLR2) should be chosen.
13
Table 7: Results from F-Tests
SLR Model
Whole Model F-Test
MLR1 Model
Equation: crime = β0 + β1 educ + u
Fmodel = 46.27
F0.05,1,340 = 3.84
Fmodel > F0.05,1,340
Unrestricted Equation: crime = β0 + β1 educ
+ β2 age
+ β3 unemploy
+ u
Restricted Equation: crime = β0 + β1 educ
+ u
Whole Model F-Test
Fmodel = 26.22
F0.05,3,338 = 2.60
Fmodel > F0.05,3,338
Partial F-Test
Fpartial = 14.37
F0.05,2,338 = 3.00
Fpartial > F0.05,2,338
MLR2 Model
Unrestricted Equation: crime = β0 + β1 educ
+ β2 age
+ β3 unemploy
+ β4
gini + β5 poverty
+ u
Restricted Equation: crime = β0 + β1 educ
+ u
Whole Model F-Test
Fmodel = 19.54
F0.05,5,336 = 2.21
Fmodel > F0.05,5,336
Partial F-Test
Fpartial = 11.44
F0.05,4,336 = 2.37
Fpartial > F0.05,4,336
5. Conclusion
The results show that our hypothesis was correct- an increase in the percent of individuals
educated at the high school level in each metropolitan area leads to a decrease in crime. Although the
impact of education on crime is indisputable within our model, the model itself shows that there is a
low level of correlation between high school attainment and crime rates overall.
The large intercept indicates that even with all factors optimized to reduced crime rates, some
crime would continue to occur. This is almost certainly due to the most basic economic conflict
between unlimited wants and limited resources; as long as individuals want what is scarce, they will
try to take from others (leading to property crime) and as long as we are stressed at all (whether from
lack of resources or other conflicts) we will lash out at others (leading to violent crimes). This can
occur no matter how educated or affluent a person is. This leads to a high intercept, and in turn, to a
looser fit to our model.
Our model is unable to encapsulate all the reasons people turn to crime. Even people who are
not desperate or who have resources or education can be influenced by passion or want more. A
14
simple model is unable to fully plot crime rates. This in turn leads to a low r-squared; there may be no
deciding factor which correlated with crime rates.
Another major factor may be the fact that our research only covers metropolitan areas.
Whereas in metropolitan areas population density leads to greater competition for jobs, rural areas
have less such competition. A high school education might be sufficient to get a job in a rural area
when there’s less competition for each individual open position, but in comparison the same
individual may not be able to find work in the city. Further research might want to cover rural
counties as well as metropolitan areas.
The low level of correlation does not detract from the results, however. There is a negative
correlation between the percent of the population which has a high school diploma and the amount
of crime committed within each metropolitan area. This could be because of one of three reasons.
First, the higher income possible due to increased education might make crime a less attractive means
to make a living. Second, crime rates might be lower because continued socialization and
indoctrination into normal society throughout high school might make people less likely to commit
violent or property crimes. Third, delaying a person’s possible entry into the criminal lifestyle until age
eighteen might restrict their evolution to property and violent crime.
The propensity to commit crime is influenced by a variety of factors. The results of this study
show that educational attainment, regardless of what function it plays in deterring crime, is a factor in
predicting the level of crime in a metropolitan city. As a result, to reduce violent and property crime
levels in cities around the nation and to shift government funding away from prisons, policy makers
should look towards educating the youth and increasing educational attainment.
15
6. Works Cited
Anderson, D. Mark. "In School And Out Of Trouble? The Minimum Dropout Age And Juvenile Crime."
Review Of Economics And Statistics 96.2 (2014): 318-331. EconLit. Web. 5 Oct. 2016.
FBI:Uniform Crime Reporting Database. “2015 Crime in the United States.” Table 6: Crime in the
United States by Metropolitan Statistical Area (2015). Web. 24 Sept. 2016.
Fella, G., and G. Gallipoli. "Education and Crime over the Life Cycle." The Review of Economic Studies
81.4 (2014): 1484-517. Web. 26 Sept. 2016.
Groot, W., and H. M. Van Den Brink. "The Effects of Education on Crime." Applied Economics 42.3
(2010): 279-89. Web. 26 Sept. 2016.
Lochner, Lance. "Non-Production Benefits of Education: Crime, Health, and Good Citizenship." (2011).
Working Paper 16722: n. pag. National Bureau of Economic Research. Web. 26 Sept. 2016.
Marlow, M. L., and A. F. Shiers. "Do Crime-Related Expenditures Crowd out Higher Education
Expenditures?" Public Finance Review 29.5 (2001): 369-93. Web. 26 Sept. 2016.
OECD. Education at a Glance 2013: OECD Indicators. OECD Publishing. (2013). Web. 24 Sept. 2016
United States Census Bureau. “Educational Attainment” American Community Survey 1-Year Estimates
(2015). Web. 1 Oct. 2016.
United States Census Bureau. “Employment Status in the Past 12 Months” American Community
Survey 1-Year Estimates (2015). Web. 5 Oct. 2016.
United States Census Bureau. “Gini Index of Income Inequality” American Community Survey 1-Year
Estimates (2015). Web. 1 Oct. 2016.
United States Census Bureau. “Median Age By Sex” American Community Survey 1-Year Estimates
(2015). Web. 5 Oct. 2016.
United States Census Bureau. “Poverty Status in the Past 12 Months By Sex By Age” American
Community Survey 1-Year Estimates (2015). Web. 1 Oct. 2016.
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Appendix
A1: STATA Output for Correlation Between Variables
A2: STATA Output for Residuals Summary Statistics
A3: STATA Output for Simple Linear Regression Model
17
A4: STATA Output for Multiple Linear Regression Models
MLR1:
MLR2:
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strengths and weaknesses
of the research).
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