This document analyzes relationships between variables related to population demographics across US states. It examines the percentage of urban population, population with long commutes over 1 hour, population with bachelor's degrees, and population with graduate degrees. It finds moderate positive linear relationships between urban population and education levels, and between commute times and education levels. Unexpectedly, it also finds a moderate positive relationship between commute times and urban population. The results suggest states with higher urban and education levels tend to have longer commute times, potentially due to traffic in urban areas limiting transportation speeds.

1. Quantitative
reasoning II -
final project
Sarah Lee • Hannah Pierce

2. Introduction

3. Variables
● Variables
○ Urban population [ %Urban ]
○ Percentage population with commute over 1 hr [ %LongCommute ]
○ Percentage population with bachelor’s degrees [ %BA ]
○ Percentage population with graduate degrees [ % MA ]
● Hypotheses
○ Negative linear relationship between %Longcommute VS %BA/MA
○ Positive linear relationship between %Longcommute VS %Urban
○ Positive linear relationship between %Urban VS %BA/MA

4. Patterns Across the United States
● %Urban
○ 1st highest D.C. at 100%
○ 2nd highest California at 95%
○ Lowest Maine with 38.7%
○ Highest urban populations on the East and West coasts
● %LongCommute
○ Highest New York at 16.6%
○ Lowest South Dakota at 2.6%
○ Highest commute times in Northeastern states
○ Lowest commute times in Midwestern states

5. Patterns Across the United States
● %BA
○ 1st highest D.C. at 50%
○ 2nd highest Massachusetts at 39%
○ Lowest West Virginia at 17.5%
○ Highest degree holders in
Northeastern states
○ Lowest degree holders in
Southeastern states
● %MA
○ 1st highest D.C. at 26.9%
○ 2nd highest Massachusetts at 16.7%
○ Lowest Arkansas at 6.3%
○ Regional trends similar to %BA

6. Univariate analysis

7. %BA
Median = 27.1%
Mean = 28%
SD = 5.7%
Distribution is
positively / right
skewed
Outlier: D.C.
Excluding outlier,
distribution is normal

8. %MA
Median = 9.4%
Mean = 10.3%
SD = 3.4%
Distribution is
positively / right
skewed
Outlier: D.C.
Excluding outlier,
distribution is similar

9. %Urban
Median = 74.2%
Mean = 74.1%
SD = 14.9%
Distribution is almost
normal
Outlier: D.C.
Excluding outlier,
distribution is similar
or slightly negative /
left skewed

10. %LongCommute
Median = 5.8%
Mean = 6.8%
SD = 14.9%
Distribution is
positively / right
skewed
Outliers: Maryland,
New Jersey, New York
Excluding outliers,
distribution is closer
to normal but still
positively / right
skewed

11. Bivariate analysis

12. %BA VS %Urban
Positive linear relationship
y = 37.88 + 1.30x
r = +0.50 (moderate)
r2
= 0.25

13. %MA VS %Urban
Positive linear relationship
y = 52.23 + 2.12x
r = +0.48 (moderate)
r2
= 0.23

14. %BA VS %LongCommute
Positive linear relationship
y = 0.86 + 0.21x
r = +0.43 (moderate)
r2
= 0.18

15. %MA VS %LongCommute
Positive linear relationship
y = 2.39 + 0.43x
r = +0.51 (moderate)
r2
= 0.26

16. %Urban VS %LongCommute
Positive linear relationship
y = 0.37 + 0.087x
r = +0.45 (moderate)
r2
= 0.21

17. Summary and investigation

18. Summary of observations of relationships
● Highest correlation between %MA and %LongCommute at
r = +0.51
● %LongCommute increases as %Urban increases
● Both are unexpected results, results are correlated
● As % graduates increases, more people live in urban areas
● Commute times increase due to high traffic in urban areas
● Walking or biking slower modes of transportation than cars,
potential increase in %LongCommute data

19. Regional Comparisons

20. Regional Comparisons

21. Regional Comparisons