stats 20 midterm 2

What does %% do in R?

It returns the remainder of division (modulo operator).

What does %/% do in R?

It returns the integer quotient of a division.

What function sets the working directory?

setwd()

What function shows your current working directory?

getwd()

How do you create a vector with the values 1, 2, and 3?

c(1, 2, 3)

c(1, 2, 3)

length()

What function gives you the type of storage for a vector?

mode()

How do you repeat a vector [1, 2] three times?

rep(c(1, 2), times = 3)

What does sample() do?

Randomly samples elements from a vector.

What does o[x] do if x is numeric?

Returns elements at positions specified in x.

What does o[-x] do?

Returns all elements except the ones at positions in x.

How do you coerce a vector to numeric?

as.numeric(x)

What does logical() create?

An empty logical vector.

What function creates a matrix in R?

matrix()

How do you access the second row of a matrix A?

A[2, ]

What does summary() return for a numeric vector?

Min, 1st Qu., Median, Mean, 3rd Qu., Max

What function converts characters to numbers?

as.numeric()

What function gets the sine of a value?

sin()

What does rev() do?

Reverses a vector.

What is NaN?

"Not a Number" – result of invalid math like 0/0.

How do you check if a value is NA?

is.na(x)

How do you test if a number is infinite?

is.infinite(x)

What does ?mean do?

Opens help for the mean() function.

What’s the difference between ? and ???

? searches by function name; ?? does a broader search (keywords, topics).

What does which() do?

Returns indices of TRUE values in a logical vector.

How do you check if all elements are TRUE?

all(x)

How do you check if two objects are nearly equal?

all.equal(x, y)

What function creates a data frame?

data.frame()

How do you extract a column from a data frame called df named "age"?

df$age

What function returns the number of rows?

nrow(df)

What does str(df) show?

The structure of the data frame, including types and samples of data.

What does ggplot() do?

Initializes a ggplot object.

What function sets the mapping of x/y to variables?

aes()

What function saves a plot to file?

ggsave()

What are the three main loop/control structures?

for(), if()/else, while()

What function exits the current iteration in a loop early?

next

What function exits the entire loop?

break

How do you define a function?

function(x) { … }

What do |> and %>% do?

Pipe the result of one expression into the next.

What does ifelse() do?

Vectorized if-else conditional; returns values based on a logical test.

What does unlist() do?

Flattens a list to an atomic vector.

How do you check if a value is in a vector?

x %in% y

Write an R function isleapyear() that takes a single year as input and returns TRUE if it's a leap year, and FALSE otherwise. A year is a leap year if it is divisible by 4, but not divisible by 100 unless also divisible by 400.

is_leap_year <- function(year) {
  (year %% 4 == 0) & ((year %% 100 != 0) | (year %% 400 == 0))
}

What is the output of isleapyear(3)?

[1] FALSE

Explanation:
3 is not divisible by 4, so it is not a leap year.

What is the output of isleapyear(8)?

[1] TRUE

Explanation:
8 is divisible by 4, and not divisible by 100, so it is a leap year.

What is the output of isleapyear(200)?

[1] FALSE

Explanation:
200 is divisible by 100 but not by 400, so it is not a leap year.

What is the output of isleapyear(800)?

[1] TRUE

Explanation:
800 is divisible by 4, by 100, and by 400. It is a leap year.

Given the nested list big_list, how is the data structured?

The list big_list has four top-level elements named:

1. "None" – an empty list

2. "One" – a list containing a single number: 1

3. "Star Wars" – a list with:

   • A sublist called "characters" (with nested lists for Obi Wan, Luke Skywalker, and R2D2)

   • A sublist called "movies" (a list of 3 movie titles)

4. "Four" – a character vector: "Even", "more", "entries"

So big_list looks like this at the top level:

list(

"None" = list(),

"One" = list(1),

"Star Wars" = list( # <-- third element

characters = list( # <-- first element inside

"Obi Wan" = list(species = "human", movies = 1:6),

"Luke Skywalker" = list(species = "human", movies = 4:6),

"R2D2" = list(species = "robot", movies = 1:6)

),

movies = list(...) # <-- second element inside

),

"Four" = c("Even", "more", "entries")

)

How do you extract the character "robot" from big_list using only numeric indices?

big_list[[3]][[1]][[3]][[1]]

Correct Output:

[1] "robot"

What does each step in big_list[[3]][[1]][[3]][[1]] do?

1. big_list[[3]] → accesses the "Star Wars" list (3rd element).
2. [[1]] → gets the "characters" sublist (first item inside "Star Wars").
3. [[3]] → gets the R2D2 sublist (3rd character).
4. [[1]] → retrieves the value of the first item in R2D2, which is "robot" under "species".

Write an R function imperial_to_metric() that takes two non-negative scalar arguments feet and inches and returns the total height in centimeters. Assumes: 12 inches = 1 foot, 1 inch = 2.54 cm. Include default values for both inputs.

imperial_to_metric <- function(feet = 0, inches = 0) {
  total_inches <- feet * 12 + inches
  c(cm = total_inches * 2.54)
}

Explanation: Converts total height to inches first, then multiplies by 2.54 to get centimeters. Returns a named vector with name \"cm\"

What is the output of the following call?

imperial_to_metric(feet = 1)

cm 30.48

Explanation: 1 foot = 12 inches → 12 * 2.54 = 30.48 cm

What is the output of the following call?

imperial_to_metric(inches = 2)

cm 5.08

Explanation: 2 inches * 2.54 = 5.08 cm

What is the output of the following call?
```r
imperialtometric(feet = 1, inches = 2)

cm 35.56

Explanation: 1 foot = 12 inches → 12 + 2 = 14 inches, then 14 * 2.54 = 35.56 cm

Write an R function metrictoimperial() that:

Takes a single non-negative scalar input cm (centimeters)

Converts the value into feet and inches

Returns a named numeric vector of length 2: c(feet = …, inches = …)

Uses default input value cm = 0

metric_to_imperial <- function(cm = 0) {
  total_inches <- cm / 2.54
  feet <- total_inches %/% 12
  inches <- total_inches %% 12
  c(feet = feet, inches = inches)
}

Explanation:

cm / 2.54 converts centimeters to inches

total_inches %/% 12 computes full feet

total_inches %% 12 gives the remaining inches

What is the output of the following?
metrictoimperial(30.48)

feet inches
1 0

Explanation:

30.48 cm is exactly 12 inches (1 foot). This function avoids outputting “0 feet and 12 inches,” which would be incorrect formatting.

What is the output of the following?
metrictoimperial(5.08)

feet inches
0 2

Explanation:

5.08 cm is exactly 2 inches. Correctly returns no feet and 2 inches.

What is the output of the following?
metrictoimperial(35.56)

feet inches
1 2

Explanation:

35.56 cm = 14 inches → 1 foot + 2 inches. This output avoids “26 inches” and formats the result correctly.

What does %% do in R?

It returns the remainder of division (modulo operator).

What does %/% do in R?

It returns the integer quotient of a division.

What function sets the working directory?

setwd()

What function shows your current working directory?

getwd()

How do you create a vector with the values 1, 2, and 3?

c(1, 2, 3)

What function returns the number of elements in a vector?

length()

What function gives you the type of storage for a vector?

mode()

How do you repeat a vector [1, 2] three times?

rep(c(1, 2), times = 3)

What does sample() do?

Randomly samples elements from a vector.

What does o[x] do if x is numeric?

Returns elements at positions specified in x.

What does o[-x] do?

Returns all elements except the ones at positions in x.

How do you coerce a vector to numeric?

as.numeric(x)

What does logical() create?

An empty logical vector.

What function creates a matrix in R?

matrix()

How do you access the second row of a matrix A?

A[2, ]

What does IQR() compute?

The interquartile range.

How do you get the cumulative sum of a vector?

cumsum(x)

What does summary() return for a numeric vector?

Min, 1st Qu., Median, Mean, 3rd Qu., Max

What function converts characters to numbers?

as.numeric()

What function gets the sine of a value?

sin()

What does rev() do?

Reverses a vector.

What is NaN?

"Not a Number" – result of invalid math like 0/0.

How do you check if a value is NA?

is.na(x)

How do you test if a number is infinite?

is.infinite(x)

What does ?mean do?

Opens help for the mean() function.

What’s the difference between ? and ???

? searches by function name; ?? does a broader search (keywords, topics).

What does which() do?

Returns indices of TRUE values in a logical vector.

How do you check if all elements are TRUE?

all(x)

How do you check if two objects are nearly equal?

all.equal(x, y)

What function creates a data frame?

data.frame()

How do you extract a column from a data frame called df named "age"?

df$age

What function returns the number of rows?

nrow(df)

What does str(df) show?

The structure of the data frame, including types and samples of data.

What does ggplot() do?

Initializes a ggplot object.

What function sets the mapping of x/y to variables?

aes()

What function saves a plot to file?

ggsave()

What are the three main loop/control structures?

for(), if()/else, while()

What function exits the current iteration in a loop early?

next

What function exits the entire loop?

break

How do you define a function?

function(x) { … }

What do |> and %>% do?

Pipe the result of one expression into the next.

What does ifelse() do?

Vectorized if-else conditional; returns values based on a logical test.