# Homework Assignment 1 Solution

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## Description

Description

In this assignment, you will analyze a subset of the U.S. Department of Education’s College Scorecard Data1. This dataset combines demographic and economic information for all 4-year colleges in the U.S. in 2013. Each row corresponds to one college campus. A description of all features in this dataset is included at the end of this document.

The dataset is available on Canvas as the file college_scorecard_2013.rds.

Questions

Use R to find answers to all of the following questions (that is, don’t do any by hand or by point-and-click).

Save your code in an R script. Try to complete at least one every day until the assignment is due.

1. How many observations are recorded in the dataset? How many colleges are recorded?

1. How many features are there? How many of these are categorical? How many are discrete? Are there any other kinds of features in this dataset?

1. How many missing values are in the dataset? Which feature has the most missing values? Are there any patterns?

1. Are there more public colleges or private colleges recorded? For each of these, what are the proportions of highest degree awarded? Display this information in one graph and comment on what you see.

2. What is the average undergraduate population? What is the median? What are the deciles? Display these statistics and the distribution graphically. Do you notice anything unusual?

1. Compare tuition graphically in the 5 most populous states. Discuss conclusions you can draw from your results.

Part a. What is the name of the university with the largest value of avg_sat?

Part b. Does the university with the largest amount of undergrad_pop have open admissions?

Part c. List the zip code of the public university with the smallest value of avg_family_inc.

Part d. Does the university you found in part b. also have the largest amount of grad_pop?

1. For schools that are for-profit in ownership and issue Bachelor’s degrees as their primary_degree, do the following:

Part a. Visualize revenue_per_student and spending_per_student and describe the relation-ship. What issues may arise when fitting a linear regression model?

Part b. Create a new variable called total_net_income. Think carefully about how this variable would be calculated. Visualize the top 5 earning schools.

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9. Now, examine the relationship between avg_sat and admission for all schools.

Part a. Use an appropriate plot to visualize the relationship. Split the data into two groups based on their combination of avg_sat and admission. Justify your answer. Hint: How does the variance of admission depend on values of avg_sat?. Define this variable as group.

Part b. Using code to justify your answers, comment on how the following continuous variables change depending on group:

1. med_10yr_salary

1. The percentage of race_white and race_asian combined

1. The percentage of graduate students enrolled at a university

Part c. Using code to justify your answers, comment on whether the categorical variables are dependent or independent of group:

1. main_campus

1. ownership

1. Whether the university has more than 1 branch or not

1. Examine the relationship between avg_10yr_salary using avg_family_inc for all schools.

Part a. Use an appropriate plot for these two variables. Fit a linear regression model that predicts avg_10yr_salary using avg_family_inc. Add this line to the plot you used. Investigate the groups of points that may be affecting the regression line.

Part b. Describe a categorical variable that would improve the fit of the regression line based on your investigation in part a. What would the levels of this variable be?

Assemble your answers into a report. Please do not include any raw R output. Instead, present your results as neatly formatted 3 tables or graphics, and write something about each one. You must cite your sources. Your report should be no more than 8 pages including graphics, but excluding code and citations. The page limit is deliberately low so that you will think carefully about what information is important to include.

What To Submit

Email a digital copy to spring18stat141a@gmail.com. The digital copy must contain your report (as a PDF) and your code (as one or more R scripts).

Additionally, submit a printed copy to the box in the statistics department office4 . The printed copy must contain your report and your code (in an appendix). Please print double-sided to save trees. It is your responsibility to make sure the graphics are legible in the printed copy!

Data Documentation

The dataset contains the following features:

unit_id unique campus ID number

ope_id unique college ID number

main_campus whether this the main campus

branches number of campuses for this college

2These features can but do not necessarily have to be present in the dataset! 3See the graphics checklist on Canvas.

44th floor of Mathematical Sciences Building

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name name

city city

state state

zip zip code

online_only whether college is online-only

primary_degree most common degree awarded

highest_degree highest degree awarded

ownership ownership (public, nonprofit, or for profit)

avg_sat mean SAT score of students

cost estimated total cost without financial aid

net_cost estimated total cost with financial aid

tuition in-state tuition cost

tuition_nonresident out-of-state tuition cost

revenue_per_student amount college earns per student

spend_per_student amount college spends per student

avg_faculty_salary mean faculty salary

ft_faculty % of full-time faculty

retention % of students that stay more than 1 year

completion % of students that graduate within 6 years

fed_loan % of students that take out federal loans

pell_grant % of students that receive Pell grants

avg_family_inc mean family income of students

med_family_inc median family income of students

avg_10yr_salary mean salary of students 10 years after starting college

sd_10yr_salary standard deviation of salary of students 10 years after starting college

med_10yr_salary median salary of students 10 years after starting college

med_debt median debt of students at graduation

med_debt_withdraw median debt of students at withdrawal

default_3yr_rate % of students that default on loans after 3 years

repay_5yr_rate_withdraw % of withdrawn students that have partially or completely repaid loans after 5 years

repay_5yr_rate % of graduated students that have partially or completely repaid loans after 5 years

avg_entry_age mean student age at entry

veteran % of students that are veterans

first_gen % of first-generation college students

male % of male students

female % of female students

race_white % of white students

race_black % of black students

race_hispanic % of Hispanic students

race_asian % of Asian students

race_native % of Native American students

race_pacific % of Pacific Islander students

race_other % of students of mixed/unspecified race

For more detailed information, see the original documentation provided by the Department of Education:

The clean_college_scorecard.R file in the extras/ directory on Canvas shows how feature names in this dataset correspond to the original.

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Relevant Functions

getwd(), setwd(), readRDS(), names(), colnames(), rownames(), nrow(), ncol(), dim(), length(), str(), summary(), table(), prop.table(), mean(), median(), sd(), quantile(), fivenum(), cor(), max(), min(), plot(), boxplot(), density(), hist(), dotchart(), matplot(), legend(), smoothScatter(), par(), which.max(), which.min(), order(), sort(), is.na(), typeof(), class(), sapply()

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