Exam 1 Review

Lecture 12

Prof. Mine Çetinkaya-Rundel

Duke University
STA 199 - Fall 2026

September 30, 2026

Warm-up

While you wait: Participate 📱💻

• Check your email (and your spam folder) for an email from TEAMMATES

• Fill out your peer evaluation for your team members

If you fail to submit your feedback, you’re not eligible to receive the points they give you.

From last time

• Go to your ae project in Positron.

• If you haven’t yet done so, make sure all of your changes up to this point are committed and pushed, i.e., there’s nothing left in your source control pane.

• If you haven’t yet done so, pull to get today’s application exercise file: ae-07-chronicle-scrape-I.qmd.

• Work through the application exercise in class, and render, commit, and push your edits by the end of class.

Exam 1 review

Exam 1

Exam 1 is on Wednesday, starts promptly at 1:25 pm!

• Covers all material up to and including today’s lecture

• Sample exam + model solutions for select HW questions are posted

• Exam will be in class, closed book, no calculators, no computers, just 1 notes sheet

• Notes sheet: 8.5x11, both sides, hand written or typed, any content you want, must be prepared by you

• We’ll direct you to your seat so get here early to allow time to get settled and read the instructions

Types of questions

• Multiple-choice:
  • Some will be single best answer, no partial credit
  • Some will be at least one correct answer, with partial credit, and clearly identified with “Select all that apply”
• Open-ended:
  • Short answer, show your work, justify your reasoning
  • With partial credit

Q1: Variable types

blizzard_salary has 409 rows and 4 columns. Each row is a worker who completed the spreadsheet. Which statements are correct? Select all that apply.

1. The dataset has 399 rows.
2. The dataset has 4 columns. Correct
3. Each row represents a Blizzard Entertainment worker who filled out the spreadsheet. Correct
4. percent_incr is numerical and discrete.
5. salary_type is numerical.
6. annual_salary is numerical. Correct
7. performance_rating is categorical and ordinal. Correct

Q9: Where did the observations go? — question

A friend notices that the total number of observations in this plot seems lower than the total in blizzard_salary (409 workers). What might be going on here? Explain your reasoning.

Observations with missing values for both variables won’t be represented on the plot.

Q13: Reviewing an interpretation — question

For Top performers, a team writes: “The relationship is positive, having a higher salary results in a higher percent increase. There is one clear outlier.” Which peer review notes are accurate and helpful? Select all that apply.

1. The interpretation is complete and perfect.
2. It doesn’t mention the direction.
3. It doesn’t mention the form, which is linear. Correct.
4. It doesn’t mention the strength, which is somewhat strong. Correct.
5. There isn’t a clear outlier; identify any potential outlier by its salary and/or percent increase. Correct.
6. The interpretation is causal; observational data do not establish which variable causes the other or rule out other explanations. Correct.

Q16: Which bar plot?

Which plot is produced by this code? Correct: D.

ggplot(penguins, aes(x = island, fill = species)) +
  geom_bar()

Q17: Reading a tibble

Based on this output, which statements must be true? Select all that apply.

# A tibble: 336,776 × 19
    year month   day arr_delay carrier dep_time sched_dep_time
   <int> <int> <int>     <dbl> <chr>      <int>          <int>
 1  2013     1     1        11 UA           517            515
 2  2013     1     1        20 UA           533            529
 3  2013     1     1        33 AA           542            540
 4  2013     1     1       -18 B6           544            545
 5  2013     1     1       -25 DL           554            600
 6  2013     1     1        12 UA           554            558
 7  2013     1     1        19 B6           555            600
 8  2013     1     1       -14 EV           557            600
 9  2013     1     1        -8 B6           557            600
10  2013     1     1         8 AA           558            600
# ℹ 336,766 more rows
# ℹ 12 more variables: dep_delay <dbl>, arr_time <int>,
#   sched_arr_time <int>, flight <int>, tailnum <chr>,
#   origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>,
#   hour <dbl>, minute <dbl>, time_hour <dttm>

1. flights is a tibble. Correct.
2. flights has 10 rows.
3. flights has 8 columns.
4. carrier is a character variable. Correct.
5. There are no missing data in flights.

Q27: Summing a condition

Which statements about the code and its result are true? Select all that apply.

movies |>
  summarize(sum(release_country == "United States"))

# A tibble: 1 × 1
  `sum(release_country == "United States")`
                                      <int>
1                                       435

1. It evaluates whether each release_country equals "United States", resulting in logical values. Correct.
2. It filters out rows where release_country is not "United States" and counts the remaining rows.
3. It sums the logical values, treating each TRUE as 1 and each FALSE as 0. Correct.
4. It results in a character vector.
5. The result shows 435 movies released in the United States. Correct.

Q29: A 6 × 6 result

movies |>
  count(rating, genre) |>
  pivot_wider(names_from = genre, values_from = n, values_fill = 0)

# A tibble: 6 × 6
  rating    Other Drama Action Comedy Horror
  <fct>     <int> <int>  <int>  <int>  <int>
1 G             5     1      1      1      0
2 PG           38    13     10     18      0
3 PG-13        19    25     35     35      0
4 R            45    50     57     96     21
5 NC-17         1     2      0      1      0
6 Not Rated     4    11      4      6      1

Which statements are true? Select all that apply.

1. The code counts movies in each rating and genre combination. Correct.
2. The code sorts the results in descending order.
3. Each row of the output is a movie.
4. The output shows six distinct ratings in the dataset. Correct.
5. The code reduces the number of variables and observations in the movies data frame to six.

Q31: Reshaping inflation data — question

country_inflation has 38 rows and 34 columns: one row per country, a country column, and annual inflation columns for 1993–2025.

country_inflation_long <- country_inflation |>
  pivot_longer(
    cols = !country,
    names_to = "year",
    names_transform = as.numeric,
    values_to = "inflation_rate"
  )

How many rows and columns does the result have? Show where each number comes from. What does each row represent, what did pivot_longer() do, and what does names_transform = as.numeric accomplish?

Q31: Reshaping inflation data — answer

Rows: 1,254. Columns: 3. Each row represents one country in one year.

1. 38 is the number of countries (the original rows).
2. 34 − 1 = 33 columns are year columns: exclude the one country column. Equivalently, 2025 − 1993 + 1 = 33 years.
3. Each country becomes 33 rows, so the total is:

\[38 \times 33 = 38 \times 30 + 38 \times 3 = 1{,}140 + 114 = 1{,}254\]

The output columns are country + year + inflation_rate = 3:

• country is retained and repeated for each year.
• The 33 old column names become values in year.
• Their cell values become values in inflation_rate.

Missing inflation values still get rows; this code does not drop them.

Q32: Ratios and the top five — question

country_inflation |>
  filter(!is.na(`1993`), !is.na(`2025`)) |>
  mutate(inf_ratio = `2025` / `1993`) |>
  select(country, inf_ratio) |>
  arrange(desc(inf_ratio)) |>
  slice_head(n = 5)

# A tibble: 5 × 2
  country        inf_ratio
  <chr>              <dbl>
1 New Zealand         2.20
2 Australia           1.64
3 Denmark             1.51
4 Ireland             1.50
5 United Kingdom      1.48

Part 1: What does the resulting data frame represent? What does New Zealand’s inf_ratio of 2.20 mean?

Part 2: What would change if the filter() step were removed? Why could that be misleading?

Q32: Ratios and the top five — answer

Part 1: These are the five countries with the largest 2025-to-1993 inflation ratios, in descending order.

• A ratio of 2.20 means New Zealand’s 2025 inflation rate was 2.20 times its 1993 rate (120% higher). It does not mean the 2025 inflation rate was 2.20%.
• arrange(desc(inf_ratio)) puts the largest ratios first. slice_head(n = 5) keeps the first five rows in that order.

Part 2: Without filter(), six countries would have NA ratios because at least one of their two rates is missing.

• arrange() puts these NAs last. For these data, the same five countries would still be returned.
• The top-five table cannot reveal whether an absent country has a smaller ratio or lacks data. Filtering makes the exclusion explicit; report that the ranking uses 32 of 38 countries.

Q32: What exactly does slice_head() do?

It selects rows by their current positions. It does not sort or calculate a summary.

Stage	Rows	What happened?
Start	38	One row per country
filter(...)	32	Keep countries with both endpoint rates
mutate(...)	32	Add one ratio to each row
select(...)	32	Keep two columns
arrange(desc(inf_ratio))	32	Put largest ratios first
slice_head(n = 5)	5	Keep rows 1–5

Removing only slice_head(n = 5) keeps all 32 eligible countries. It does not restore the six countries excluded by filter().

Other questions

• Q2
• Q4
• Q7
• Q8
• Q14
• Q23
• Q24
• Q28
• Q30

Exam review answers