This document discusses variables related to human development across U.S. states. It analyzes the percentage of population with bachelor's degrees (%BA), percentage with master's degrees (%MA), urban population (%Urban), and percentage with long commutes (%LongCommute) in each state. For each variable, it provides summary statistics and finds that %BA and %MA are right-skewed, %Urban follows a normal distribution, and %LongCommute is right-skewed. It hypothesizes relationships between the variables and plans univariate and bivariate analyses.

1. Quantitative Reasoning II ­ Final Project
Hannah Pierce and Sarah Lee Shan Yun
Preliminary stage
What is human development?
Human development is the concept and subsequent study of human longevity and
wellbeing as a factor of national (or global) development that takes precedent over
measurements of economic factors, such as GDP. Human development pairs easily
with social justice initiatives and plays a role in social research. This concept measures
increased wellness and opportunities as indicators of growth. Education, public health,
and public transportation infrastructure are all important topics that human development
focuses upon.
Variables
1. Urban population (%Urban)​ is described as the percentage of the population
living in cities in a given state. It is measured as a percentage (%) and​ is
calculated using World Bank ​Population​ estimates and ​urban​ ratios from the
United Nations World Urbanization Prospects via statistical estimation. 1
2. Percentage population with long commutes (%LongCommute)​ measures the
percentage (%) of the population with commute times that are 60 minutes or
longer and is obtained through surveying a representative portion of each state’s
population. This data includes active commuters (bikers, walkers, etc.) as well as
commuters taking public transportation or automobile transportation).
3. Percentage population with a bachelor's degree (%BA)​ measures the percentage
of the population (%) who hold bachelor’s degree level education (BA) or higher.
There will be a higher percentage of BA degree holders than MA degree holders
because a BA is required before an individual can pursue an MA. Education
attainment is calculated through a census of U.S. universities in each of the U.S.
states.
4. Percentage population with a graduate degree (%MA)​ measures the percentage
of the population (%) who hold masters degree level education (MA) or higher.
Education attainment is calculated through a census of U.S. universities in each
of the U.S. states.
1
"Urban Population Data." ​Urban Population Data​. The World Bank, 2015. Web. 3 Nov. 2015.
<http://data.worldbank.org/indicator/SP.URB.TOTL>

2. Patterns across U.S. states
Urban population (%Urban)
The District of Columbia has the highest urban population at 100% because the state
constitutes Washington D.C. The state with the second highest urban population is
California at 95%. The state with the lowest percentage urban population is Maine at
only 38.7%. The map shows the population density of the U.S. by county in 2010 . 2
States with the highest urban populations tend to be situated along the east and west
coasts, whilst the midwest consists of more rural populations.
Percentage population with long commutes (%LongCommute)
New York has the highest percentage of long commuters at 16.6%. Northeastern states
have some of the highest percentages of commutes over one hour. South Dakota has
the lowest percentage of long commuters at 2.6%. The Midwest, into the Northwest
have the lowest percentage of commute times over one hour.
Percentage population with a bachelor’s degree (%BA)
West Virginia has the lowest percentage of people with bachelor’s degrees at 17.5%,
while the District of Columbia has the highest percentage of citizens with bachelor’s
degrees at 50%, followed by Massachusetts at 39%. It appears that Southeastern
states tend to have lower percentages of people that hold a bachelor’s degree, while
states in the Northeast have the highest percentage of those holding bachelor’s
degrees.
Percentage population with a master’s degree (%MA)
The state with the lowest percentage of the population with a master’s degree is
Arkansas, at 6.3%. The state with the highest number of people with master’s degrees
is the District of Columbia, at 26.9%, followed by Massachusetts at 16.7%. The high and
low regional trends are similar to the measures of bachelor’s degrees.
2
"Thematic Maps, Geography." ​U.S. Census Bureau​. U.S. Census Bureau, 2010. Web. 12 Nov. 2015.
<https://www.census.gov/geo/maps­data/maps/thematic.html>.

3. Possible relationships between variables / hypotheses
From initial observations of the variables, we believe that the ​percent population with
long commutes​ will have a negative linear relationship with ​percentage population with
a bachelor’s degree​ and ​percentage population with a master’s degree​, but a positive
linear relationship with ​urban population​. For example, states with a higher ​urban
population​ are more likely to have a higher ​percent population with long commutes​. We
predict that states with higher ​urban populations​ will have a higher ​percentage
population with bachelor’s and master’s degrees​, and that those holding those degrees
live closer to work and are less likely to commute over 60 minutes to work.

4. Stage One: Univariate Analysis
Percentage population with a bachelor's degree (%BA)
Summary statistics
Column n Mean Std. dev. Median Range Min Max Q1 Q3
%BA 51 27.93333 5.723309 27.1 32.6 17.5 50.1 24.5 30.8
According to the data, the median
percentage of population with a bachelor’s
degree is 27.1% and the mean is about 28%.
41.1% of U.S. states contain populations
where 25% to 30% of people have at least a
bachelor’s level degree.
The distribution of the curve is positively
(right) skewed with most states having a
%BA population below the mean. About 70%
of the U.S. states have %BA populations
between 17.5% to 30%. Only about 30% of
U.S. states have %BA populations above
30%.
1 state, in particular, The District of
Columbia is an outlier in the data with 50.1%
of the population being bachelor degree level
holders and above.​ ​Excluding the outlier, the
data follows a normal distribution very
closely.
One standard deviation from the mean
is 22.2% and 33.7%. 84.3% of the data falls
within one standard deviation of the mean,
suggesting that the percentage of commute
times over 1 hour do not vary largely between
regions or states.

5. Percentage population with a master’s degree (%MA)
Summary statistics
Column n Mean Std. dev. Median Range Min Max Q1 Q3
%MA 51 10.323529 3.4059705 9.4 20.6 6.3 26.9 8.1 11.3
According to the data, the median
percentage of population with a master’s
degree is 9.4% and the mean is 10.3%. 51%
of U.S. states contain populations where
7.5% to 10% of people have at least a
master’s level degree.
The distribution of the curve is positively
(right) skewed with about 61% of states
having a %MA population below the mean.
More than half of U.S. states have %MA
populations between 7.5% to 10%. Only
about 38.5% of U.S. states have %MA
populations above 10%.
Again, 1 state, in particular, The District
of Columbia is an outlier in the data with
26.9% of the population being master degree
level holders and above.​ ​The data without the
outlier still shows a positive (right) skew.
One standard deviation from the mean
is 6.0% and 12.8%. 84.3% of the data falls
within one standard deviation of the mean,
suggesting that the percentage of commute
times over 1 hour do not vary largely between
regions or states.

6. Comparison of ​percentage %BA​ to %MA
Overall, there is a much lower percentage of master’s graduates in comparison
to bachelors graduates in the U.S. population. Unlike the %BA population data, %MA
population is still positively (right skewed) after excluding the outlier, which means that
there are more states with lower %MA populations and very little states with high %MA
populations relative to the data provided.

7. Urban population (%Urban)
Column n Mean Std.
dev.
Median Range Min Max Q1 Q3
%Urban 51 74.104 14.887 74.2 61.3 38.7 100 64.8 87.9
According to the distribution of the data,
the median is an urban population of 74.2%,
while the mean is not far off, at 74.1%.
The data closely follows a normal
distribution. The only outlier for the data, (by
less than 1%) is The District of Columbia
(Washington, D.C.) with an urban population
of 100%. It does not make much of a
difference to the appearance of the
distribution when it has been removed, but
the mean and standard deviation decrease to
73.586% and 14.567%. If anything, the data
has a slight negative skew to the left.
One standard deviation from the mean
is 59.3% and 89.1%. Exactly 66.7% of the
data falls within one standard deviation of the
mean (34 out of 50 states and 1 district).
The fact that the data has a near normal distribution seems logical, given that it
accounts for very different regions of one country. The East Coast has largely urban
populations, as there is a higher population density in these states than in many
Western states. The distribution reflects this trend.

8. Percentage population with long commutes (%LongCommute)
Column n Mean Std.
dev.
Median Range Min Max Q1 Q3
%Long
Commute
51 6.806 2.851 5.8 14 2.6 16.6 4.9 8.3
The mean percentage of a state
population with commutes over 1 hour in
duration is 6.81%, while the median is 5.8%
of a state’s population.
The distribution is skewed positively to
the right. With the removal of the outliers
(Maryland, 13.9%, New Jersey, 13.9%, and
New York, 16.6%), the skew is far less
drastic. The mean decreases to 6.3%, while
the median decreases to 5.75%.
For this data set, one standard deviation
from the mean is 4.0% and 9.7%. 76.5% of
the data falls within one standard deviation of
the mean, suggesting that the percentage of
commute times over 1 hour do not vary
largely between regions or states. To further
research this data set, it may be useful to
separate states by the types of transportation
used for commutes, or the average distance
traveled to work.

9. Stage two: bivariate analysis
Percentage population with a bachelor's degree (%BA) VS ​urban population (%Urban)
The data shows a positive relationship
between %BA and %Urban. As the
percentage of the population with bachelor’s
degrees increases, the percentage of urban
population increases as well.
The correlation coefficient (​r​) between
%BA and %Urban is +0.50. This shows a
moderate to strong linear relationship.
The equation for the regression line of
best fit is y = 37.88 + 1.30x.
The R­squared value (​r​2​
) between %BA
and %Urban is 0.25 indicating that 25% of
the variability of the %Urban data can be
explained by the variability of the %BA data.
Percentage population with a master’s degree (%MA) VS ​urban population (%Urban)
The data shows a positive relationship
between %BA and %Urban. As the
percentage of the population with master’s
degrees increases, the percentage of urban
population increases as well.
The correlation coefficient (​r​) between
%BA and %Urban is +0.48. This shows a
moderate to strong linear relationship.
The equation for the regression line of
best fit is y = 52.23 + 2.12x.
The R­squared value (​r​2​
) between %BA
and %Urban is 0.23 indicating that 23% of
the variability of the %Urban data can be
explained by the variability of the %MA data.

10. As predicted, the higher both %BA and %MA populations of the state, the higher
the urban population. This might be because as there are more people with degrees,
there are more people in the workforce who tend to live and work in more densely
populated urban cities. Companies also tend to congregate in urban areas and hire
college graduates.
Percentage population with a bachelor's degree (%BA) ​VS percentage population with
long commutes (%LongCommute)
The data shows a positive relationship
between %BA and %LongCommute. As the
percentage of the population with bachelor’s
degrees increases, the percentage of the
population with long commutes increases as
well.
The correlation coefficient (​r​) between
%BA and %LongCommute is +0.43. This
shows a moderate linear relationship.
The equation for the regression line of
best fit is y = 0.86 + 0.21x
The R­squared value (​r​2​
) between %BA and %LongCommute is 0.18 indicating
that 18% of the variability of the %LongCommute data can be explained by the %BA
data. The p­value of the model is 0.0018.

11. Percentage population with a master’s degree (%MA) VS ​percentage population with
long commutes (%LongCommute)
The data shows a moderate relationship
between %MA and %LongCommute. As the
percentage of the population with bachelor’s
degrees increases, the percentage of the
population with long commutes increases as
well.
The correlation coefficient (​r​) between
%MA and %LongCommute is +0.51. This
shows a moderate linear relationship.
The equation for the regression line of
best fit is y = 2.39 + 0.43x
The R­squared value (​r​2​
) between %MA and %LongCommute is 0.26 indicating
that 26% of the variability of the %LongCommute data can be explained by the
variability of the %MA data. The p­value of the model is 0.0001.
We did not expect to see a positive correlation between the variables, as we
predicted that those without bachelor’s or master’s degrees may not earn as much
money, live outside urban areas and may have to commute farther to work.
Urban population (%Urban) VS percentage population with long commutes
(%LongCommute)
The data shows a moderate relationship
between %Urban and %LongCommute. As
the percentage of the urban population
increases, the percentage of the population
with long commutes increases as well.
The correlation coefficient (​r​) between
%Urban and %LongCommute is +0.45. This
shows a moderate linear relationship.
The equation for the regression line of
best fit is y = 0.37 + 0.087x
The R­squared value (​r​2​
) between %Urban and %LongCommute is 0.21
indicating that 21% of the variability of the %LongCommute data can be explained by
the variability of the %Urban data. The p­value of the model is 0.0008.

12. We expected to see that cities with a higher urban population would have a
greater percentage of citizens with commute times over one hour, due to traffic delays.
This occurs to an extent, but the scatter plot indicates a less strong correlation than we
expected.
Stage three: summary and investigation suggestions (2­3 pages)
Summary of observations of relationships
As observed, the model with the highest correlation is between %MA and
%LongCommute with r = +0.51. At first, there seemed to be no direct explanation for
this relationship, but upon looking at the next observed model we see that the
%LongCommute increases as the %Urban increases as well. Both of these results were
unexpected and could have several explanations. The results are related, as the
percentage of graduates increases more people live in urban cities and therefore the
commute times for the populations increase. People could be travelling in cars which
could cause high traffic within urban areas. People could also be walking or biking to
work or school which are generally slower modes of transportation compared to cars
and public transportation and increase the %LongCommute data in urban areas.
Populations in more rural states, however, may tend to commute less often or live
directly in their area of work where there is less traffic congestion.
Comparison of U.S. Regions
For the purpose of regional comparisons, we have divided the 50 States into four
regions (West, Midwest, Northeast, and South) noted by W, MW, NE, and S in charts. 3
West Midwest South Northeast
Washington North Dakota Texas Maine
Oregon South Dakota Oklahoma Vermont
California Nebraska Arkansas New Hampshire
Nevada Kansas Louisiana Massachusetts
Idaho Iowa Mississippi Rhode Island
Colorado Minnesota Alabama Connecticut
New Mexico Missouri Tennessee New York
Arizona Wisconsin Kentucky Pennsylvania
Montana Illinois Georgia New Jersey
Wyoming Indiana Florida
Utah Michigan Virginia
Alaska Ohio West Virginia
Hawaii North Carolina
South Carolina
Maryland
3
Regions determined by “Statistical Groupings of States and Countries”
(https://files.acrobat.com/a/preview/616a7056­0769­4a8e­950c­78afc8f794ab)

13. When all of the data for a specific variable is viewed together, it is difficult to
conclude much about the specific regions of the United States. By dividing the regions,
we hope to gain a more conclusive understanding of the relationship between our
variables. We were most interested in looking at the regional differences between urban
population and commute time, and education level and commute time.
%Urban VS %LongCommute, by Region
W​: ​r​=0.628, ​r­squared​=0.394, ​sd​=1.407, ​p­value​=0.022, ​y​=­0.701+0.86x
MW​: ​r​=0.777, ​r­squared​=0.603, ​sd​=1.582, ​p­value​=0.003, ​y​=­10.881+0.223x
S​: ​r​=0.430, ​r­squared​=0.185, ​sd​=2.163, ​p­value​=0.096, ​y​=1.933+0.076x
NE​: ​r​=0.523, ​r­squared​=0.273, ​sd​=3.533, ​p­value​=0.149, ​y​=2.522+0.089x

14. The charts and figures above demonstrate a more detailed breakdown of the
percentage urban population versus the percentage of a state’s population with a long
commute. For all regions, save the South (with r=0.430), the correlation coefficient is
higher. The Midwest has the highest correlation coefficient and r­squared value, as well
as the lowest p­value. Midwestern states have urban populations between 50­80%
(Illinois has an 88% urban population) and 2­7% of the state’s inhabitants have a
commute over 1 hour long. This phenomena may be explained by the fact that most
citizens live near cities, and are easily able to travel between home and work. Although
it would be expected that the same hypothesis applies to the other regions, the
infrastructure of roads and availabilty of public transportation may contribute to higher
commute times for states with large urban populations. For example, for the
Northeastern states have very high urban populations (80­100%), the percentage of the
population with commutes over 1 hour long is extremely varied (4­17%). Congestion,
interstate commuting, and delays in public transportation may contribute to this data.
%BA VS %LongCommute

15. W​: r=0.321, r­squared=0.103, sd=1.712, p­value=0.284, y=2.807+0.147x
MW​: r=0.256, r­squared=0.065, sd=2.426, p­value=0.422, y=­1.025+0.223x
S​: r=0.600, r­squared=0.360, sd=1.917, p­value=0.014, y=0.436+0.273x
NE​: r=0.304, r­squared=0.092, sd=3.949, p­value=0.427, y=­0.406+0.294x
When divided by region, the data comparing the percentage of a state’s
population that has (at least) a Bachelor’s Degree and the percentage of the population
with a commute time over 1 hour appears to be less correlated than the country as a
whole. The South has the strongest correlation coefficient at 0.600. The percentage of
the population that has commutes over 1 hour is low as a whole, but commute times
appear to be higher for states with more inhabitants holding Bachelor’s degrees. Again,
this may be explained by infrastructure. It’s possible that those holding Bachelor’s
degrees tend to prefer living farther away from cities (where they work), preferring to live
in a suburban community.
These regions are grouped together because of their similarities in population,
history, industries, and more. To further develop comparisons, it would be useful to use
population density data, and to pull up information surrounding types of industry and the
most popular mode of transportation in these regions. This data can further develop
understanding about the relationships (or lack thereof) between urban population and
commute times over 1 hour, as well as education level and commute times over 1 hour.