# ECO394 Homework 1

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## Problem 1: playlists revisited

Return to our playlist data from a popular music streaming service contained in plays_top50.csv.

Part A
Consider two music streaming events: “plays Daft Punk” and “plays David Bowie”. These variables are called
daft.punk and david.bowie in this data set. Using the R functions xtabs and prop.table, make a 2×2
table of conditional probabilities, conditional on the levels of the david.bowie variable.

The bottom right
entry in your 2×2 table should display P(plays Daft Punk | plays David Bowie). Round the entries in your
table to 3 decimal places.

You should not include any R syntax in your write-up, but you will need to report the table that you generate
in the console. To transfer this table into your write-up, the simplest option is to copy and paste the table
from R’s console output.

If you do this, make sure you use a fixed-width font, like Courier, to display
the table—otherwise the columns won’t line up properly. You can also format tables in another program if
you’d prefer to do it that way (e.g., copying and pasting R table contents into Excel and adding borders for a
nicer presentation).

Part B
Are the events “plays Johnny Cash” and “plays Pink Floyd” independent? Why or why not? Provide

## Problem 2: Super Bowl ads

In February of 2021, the website fivethirtyeight.com ran a story that looked for interesting patterns in Super
Bowl ads over the years. Here’s how they described their approach:

Like millions of viewers who tune into the big game year after year, we at FiveThirtyEight LOVE
Super Bowl commercials. We love them so much, in fact, that we wanted to know everything about
them . . . by analyzing and categorizing them, of course. We dug into the defining characteristics
of a Super Bowl ad, then grouped commercials based on which criteria they shared—and let me
tell you, we found some really weird clusters of commercials.

We watched 233 ads from the 10 brands that aired the most spots in all 21 Super Bowls this
century, according to superbowl-ads.com. While we watched, we evaluated ads using seven specific
criteria, marking every spot as a “yes” or “no” for each.

Go read the full story here. Make sure to download the corresponding data set, called superbowl.csv, from our
Canvas site. (But watch the commercials at your own risk—you might not believe the levels of insensitivity
in some of these ads that passed for socially acceptable even 10 or 15 years ago.)

variable type description
year number Superbowl year
brand categorical Brand for commercial
funny categorical Contains humor
show_product_quickly categorical Shows product quickly
patriotic categorical Patriotic
celebrity categorical Contains celebrity
danger categorical Contains danger
animals categorical Contains animals
use_sex categorical Uses sexuality

Part A
The authors drew attention to a cluster of commercials that they described as “DANGER + NOT TRYING
TO BE FUNNY.” As they put it:
These ads probably aren’t what you think of first when it comes to Super Bowl commercials.
They feature danger, violence or injury, but not as the punchline of a joke. This cluster is home
to a few real tear-jerkers and some attempts at inspirational unity.

That made us wonder: what’s the relationship between danger and humor across all Super Bowl commercials
in the sample?
To address this question, please use the data to estimate the following probabilities:
• P(danger = TRUE)
• P(danger = TRUE | funny = TRUE)

• P(danger = TRUE | funny = FALSE)
Please round your numbers to two decimal places. In light of these numbers, does it seem that ads using
humor are more or less likely to feature danger than ads not using humor? Or, on the other hand, do humor
and danger look nearly independent of each other?

Part B
The article also described a cluster of ads that bizarrely seemed to juxtapose “selling with sex” and “animals.”

As the author put it:
There was a wide range of approaches in how advertisers combined these categories, though, with
some more disturbing than others. On one end are ads that sell sex while an animal happens to
be in one of the shots — the Bob Dole Pepsi ad shows him walking on the beach with his dog,
and a Budweiser ad that centers on some crabs stealing a cooler of beer makes sure to sneak in
frames of women in bikinis. These ads sell sex, and these ads have animals, but they’re not really
fundamentally intertwined.

At the other unholy end of the spectrum, though, are Bud Light ads in which a talking chimp hits
on a woman and a falcon brings back a woman’s bra to its handler after attacking a city block on
the hunt for beer. The only thing more unsettling than watching these bizarre commercials is
realizing a whole boardroom approved these concepts for what was a likely multimillion-dollar ad
spot. The commercials in this cluster really cover the full spectrum, so watch at your own risk.

Following on from this, please use the data to estimate the following probabilities. Round to two decimal
places.
• P(animals=TRUE)
• P(animals=TRUE | use_sex=TRUE)
• P(animals=TRUE | use_sex=FALSE)

In light of these numbers, does it seem that ads using sexuality are more or less likely to feature animals
than ads not using sexuality? Or, on the other hand, do use_sex and animals look nearly independent of
each other?

Part C
The authors also highlighted a cluster of ads that combined “patriotic symbolism with celebrity endorsements.”

Following on from this, please use the data to estimate the following probabilities. Round to two decimal
places.
• P(celebrity=TRUE)
• P(celebrity=TRUE | patriotic=TRUE)
• P(celebrity=TRUE | patriotic=FALSE)

In light of these numbers, does it seem that ads using patriotic symbolism are more or less likely to feature
celebrity endorsements than ads not using patriotic symbolism? Or, on the other hand, do celebrity and
patriotic look nearly independent of each other?

## Problem 3: Beauty, or not, in the classroom

The University of Texas at Austin, like every major university in the country, asks students to evaluate
their courses and professors.The profs.csv file contains data on course-instructor evaluation surveys from a
sample of 463 UT Austin courses. These data represent evaluations from 25,547 students and most major

The data frame also includes information on characteristics of each course and facts
about the professors such as seniority and demographics. Also included is a rating of each instructor’s physical
attractiveness, as judged by a panel of six students (3 males, 3 females) who were shown photos of the
instructors. Key variables in the prettyprofs.csv data frame are:

• eval: the instructor’s average teaching evaluation score, on a scale of 1 to 5, for courses in the sample
• beauty: the six panelists’ average rating of the professor’s physical attractiveness, shifted to have a
mean of zero. For example, 2 is two points above average and -1 is one point below average.
• minority: is the professor from a non-white racial or ethnic minority?

• age: the professor’s age in years
• gender: indicator of the professor’s gender
• credits: indicator of whether the course is a single-credit elective (“single”) or an academic course
(“more”)
• division: indicator of whether the course is a lower or upper division course

• native: indicator of whether the professor is a native English speaker
• tenure: indicator of whether the professor has tenure/is on the tenure track, or not
• students: the number of students who participated in the course evaluation survey
• allstudents: the number of students enrolled in the course
• prof: unique identifier variable for the professor

Use these data to address the following questions by creating plots and/or calculating summary statistics.

Format the plot professionally with clear labeling and consideration of best practices for effective plots.
Include in your write-up an image of each plot along with an informative caption below each plot. The
caption may be typed in your write-up below the plot and does not have to be generated using ggplot’s
caption feature.

The caption should consist of 1-2 sentences describing key features of the plot (if these are
not already clear from the chart title and labels) and a short summary of key takeaways from your plot in its
relevant context. Think of this caption as a walkthrough for your plot audience.

Part A. Create a histogram to display the overall data distribution of course evaluation scores.

Part B. Use side-by-side boxplots to show the distribution of course evaluation scores by whether or not the
professor is a native English speaker.

Part C. Use a faceted histogram with two rows to compare the distribution of course evaluation scores for
male and female instructors.

Part D. Create a scatterplot to visualize the extent to which there may be an association between the
professor’s physical attractiveness (x) and their course evaluations (y).

## Problem 4: SAT scores for UT students

The data in utsat.csv contains the SAT scores and graduating college GPAs for every UT student who
entered UT in a specific, recent year (it’s definitely this century, but I’m not saying which just to maximize
data anonymity here), and went on to graduate from UT within 6 years.

The variables in this data set are:
• SAT.V: score on the verbal section of the SAT (200-800)
• SAT.Q: score on the quantitative section of the SAT (200-800)
• SAT.C: combined SAT score
• School: college or school at which the student first matriculated (not necessarily where they ended up)
• GPA: college GPA upon graduation, on a 4-point scale
• Status: this should be G, for graduated, for everyone in this data set

Your task in this problem is to make a single table of summary statistics of this data. The table should show
the following summary statistics for SAT verbal scores, SAT math scores, and graduating GPA across the
whole sample: mean, standard deviation, inter-quartile range (IQR), 5th percentile, 25th percentile, median
(50th percentile), 75th percentile, and 95th percentile.

Your table should have three rows (SAT Verbal, SAT Quantitative, GPA) and 8 columns of numbers (one
column for each summary statistic). Use R to calculate these summary statistics, and then format them
into a nice, professional-looking table using a program like Word, Excel, Google Sheets, etc. Paste this
Include a caption for your table.

The caption may be typed in your write-up below the table and does not
have to be generated using an R command. The caption should consist of 2-3 sentences describing what the
table shows. Think of this as an orientation to the table for a reader who’s encountering it for the first time.

## Problem 5: bike sharing

Bike-sharing systems are a new generation of traditional bike rentals where the whole process from rental
to return is automatic. There are thousands of municipal bike-sharing systems around the world (e.g. Citi
bikes in NYC or “Boris bikes” in London), and they have attracted a great deal of interest because of their
important role in traffic, environmental, and health issues—especially in the wake of the Covid-19 pandemic,
when ridership levels on public-transit systems have plummeted.

These bike-sharing systems also generate a tremendous amount of data, with time of travel, departure, and
arrival position recorded for every trip. This feature turns bike sharing system into a virtual sensor network
that can be used for sensing mobility patterns across a city.

Bike-sharing rental demand is highly correlated to environmental and seasonal variables like weather conditions,
day of week, time of year, hour of the day, and so on. In this problem, you’ll look at some of these demanddriving factors using the bikeshare.csv data from the course Canvas page. This data set contains a two-year
historical log (2011 and 2012) from the Capital Bikeshare system in Washington D.C.

The raw data is publicly
available at http://capitalbikeshare.com/system-data. These data have been aggregated on an hourly and
daily basis and then merged with weather and seasonal data.

The variables in this data set are as follows:
• instant: unique record identifier for each row
• dteday: date
• season: season (1:spring, 2:summer, 3:fall, 4:winter)
• yr: year (0: 2011, 1:2012)
• mnth: month (1 to 12)
• hr: hour (0 to 23)
• holiday: whether the day is holiday or not

• weekday: day of the week (1 = Sunday)
• workingday: if day is neither weekend nor holiday is 1, otherwise is 0.
• weathersit: a weather situation code with the following values
– 1: Clear, Few clouds, Partly cloudy, Partly cloudy
– 2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist
– 3: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds
– 4: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog

• temp: Normalized temperature in Celsius. The actual values are divided by 41 (max)
• total: count of total bike rentals that hour, including both casual and registered users

Your task in this problem is to prepare three figures. To make these figures, you will need to combine the
ideas from our lesson on Plots with our lesson on Data wrangling. In other words, you won’t be able to make
these plots by calling ggplot on the raw data we’ve provided. First, you’ll need to use some of our six key
1
If you’re using RMarkdown, feel free to read up on the kable function in the knitr library.

You can see an example of how
I used this function in our course packet here. And if you ever need help with RMarkdown, just ask!
5
data verbs from the Data Wrangling lesson to get the data into an appropriate form. Only then will you
actually be able to create these plots.

• Plot A: a line graph showing average hourly bike rentals (total) across all hours of the day (hr).
• Plot B: a faceted line graph showing average bike rentals by hour of the day, faceted according to
whether it is a working day (workingday).

• Plot C: a faceted bar plot showing average ridership (y) during the 9 AM hour by weather situation
code (weathersit, x), faceted according to whether it is a working day or not. (Remember that you
can focus on a specific subset of rows of a data set using filter.)

Your write-up should include each plot, together with an informative caption (i.e., written paragraph) below
each plot. Think of this caption paragraph as a walkthrough for your plot audience – perhaps what you would
say in a live presentation to incorporate the plot into your narrative.

Your caption should clearly explain the
plot itself (e.g., what the axes represent and what the panels show). Don’t forget to specify variable units.

The caption should also contain a one-sentence take-home lesson of what we have learned about ridership
patterns from the plot.