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DS-UA 201: Final Exam
Devyani Rastogi - dr3158 - 001
Due December 20, 2023 at 5pm
Instructions
You should submit your write-up (as a knitted .pdf along with the accompanying .rmd file) to the
course website before 5pm EST on Wednesday, Dec 20th Please upload your solutions as a .pdf file
saved as
Yourlastname_Yourfirstname_final.pdf
.In addition, an electronic copy of your .Rmd
file (saved as
Yourlastname_Yourfirstname_final.Rmd
) should accompany this submission.
Late finals will not be accepted,
so start early and plan to finish early
.
Remember that exams often take longer to finish than you might expect.
This exam has
3
parts and is worth a total of
100 points
. Show your work in order to receive
partial credit.
Also, we will penalize uncompiled .rmd files and missing pdf or rmd files by 5 points.
In general, you will receive points (partial credit is possible) when you demonstrate knowledge
about the questions we have asked, you will not receive points when you demonstrate knowledge
about questions we have not asked, and you will lose points when you make inaccurate statements
(whether or not they relate to the question asked).
Be careful, however, that you provide an
answer to all parts of each question.
You may use your notes, books, and internet resources to answer the questions below. However,
you are to work on the exam by yourself. You are prohibited from corresponding with any human
being regarding the exam (unless following the procedures below).
The TAs and I will answer clarifying questions during the exam. We will not answer statistical
or computational questions until after the exam is over. If you have a question, send email to all
of us. If your question is a clarifying one, we will reply. Do not attempt to ask questions related
to the exam on the discussion board.
1
Problem 1 (100 points)
In this problem, you will examine whether family income affects an individual’s likelihood to enroll in college
by analyzing a survey of approximately
4739
high school seniors that was conducted in 1980 with a follow-up
survey taken in 1986.
This dataset is based on a dataset from
Rouse, Cecilia Elena.
“Democratization or diversion?
The effect of community colleges on
educational attainment.” Journal of Business & Economic Statistics 13, no. 2 (1995): 217-224.
The dataset is
college.csv
and it contains the following variables:
•
college
Indicator for whether an individual attended college. (Outcome)
•
income
Is the family income above USD 25,000 per year (Treatment)
•
distance
distance from 4-year college (in 10s of miles).
•
score
These are achievement tests given to high school seniors in the sample in 1980.
•
fcollege
Is the father a college graduate?
•
tuition
Average state 4-year college tuition (in 1000 USD).
•
wage
State hourly wage in manufacturing in 1980.
•
urban
Does the family live in an urban area?
Question A (35 points)
Draw a DAG of the variables included in the dataset, and explain why you think arrows between variables
are present or absent. You can use any tool you want to create an image of your DAG, but make sure you
embed it on your compiled .pdf file. Assuming that there are no unobserved confounders, what variables
should you condition on in order to estimate the effect of the treatment on the outcome, according to the
DAG you drew? Explain your decision in detail. In your explanation, provide a definition of confounding.
library
(dagitty)
# Define the DAG
dag
<-
dagitty
(
"dag {
income -> college
fcollege -> income
fcollege -> college
income -> score
score -> college
distance -> income
distance -> college
urban -> distance
urban -> income
urban -> college
wage -> income
tuition -> college
}"
,
layout =
TRUE
)
# Plot the DAG
plot
(dag)
2
college
distance
fcollege
income
score
tuition
urban
wage
1.
Income
→
College:
This arrow suggests that family income directly affects the likelihood of college
enrollment, which is the primary causal effect we are interested in.
2. Fcollege
→
Income & College: Having a father who attended college (fcollege) likely influences both
family income and the child’s likelihood of attending college, due to factors like higher earning potential
and valuing education.
3. Income
→
Score: This suggests that higher family income can lead to better academic scores, possibly
due to better educational resources.
4. Score
→
College: High scool academic scores directly impact college admission chances due to the
college cut-off percentages.
5. Distance
→
Income & College: Geographic distance from college might affect family income (e.g., rural
vs. urban income disparities) and the practicality of attending college.
6. Urban
→
Distance, Income & College:
Urban living affects the distance to college, family income
levels, and access to college education.
7. Wage
→
Income:
Indicates that state minimum wages are a component of or influence on family
income.
8. Tuition
→
College: The cost of tuition directly impacts the feasibility of college enrollment.
By the backdoor criterion, all the backdoor paths from the ‘income’ (treatment) to ‘college’ (outcome) must
be blocked in order for the effect of family income on college enrollment to be identifiable. A path is blocked
when either it contains a non-collider that we condition on, or when it contains a collider that we do not
condition on. In our case, the variables ‘fcollege’, ‘distance’, and ‘urban’ are non-colliders or confounders,
i.e. variables that influences both the treatment and the outcome. Therefore, we must condition on these
variables to understand the causal effect.
3
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