Homework Instructions

Below are the problems for Homework 1. Please write your solutions inside the provided code blocks.

Note: R will not automatically display results when you assign values to an object.
To show results, either call the object by name or use print().

When finished:

  1. Knit your R Markdown file into a PDF or HTML document.
  2. Submit both the knitted file and this .Rmd file to Canvas.

Problem 1

Perform the following arithmetic operations and include the code and results in your report:

  1. Add two numbers (5 points)
  2. Subtract two numbers (5 points)
  3. Multiply two numbers (5 points)
  4. Divide two numbers (5 points)
#Your code here

# a. Add two numbers
result_add <- 10 + 5
result_add
## [1] 15
# b. Subtract two numbers
result_sub <- 20 - 7
result_sub
## [1] 13
# c. Multiply two numbers 
result_mul <- 8 * 6
result_mul
## [1] 48
#d. Divide two numbers 
result_div <- 40 / 8
result_div
## [1] 5

Problem 2

Create two vectors x = c(10, 5, 3.5, 2) and y = c(2, 7, 1.5, 4) and perform the following:

  1. Calculate the element-wise sum of the two vectors x and y. (5 points)
  2. Subtract vector y from vector x. (5 points)
  3. Multiply the corresponding elements of x and y (element-wise multiplication). (5 points)
  4. Divide each element of vector x by the corresponding element of vector y. (5 points)
  5. Calculate the modulo (remainder) of each element in vector x divided by the corresponding element in vector y. (10 points)
#Your code here

#Create the vectors
x <- c(10, 5, 3.5, 2)
y <- c(2, 7, 1.5, 4)

#display vectors
x
## [1] 10.0  5.0  3.5  2.0
y
## [1] 2.0 7.0 1.5 4.0
# a. add vectors (element-wise)
result_add <- x + y
result_add
## [1] 12 12  5  6
# b. subtract vectors (element-wise)
result_sub <- x - y
result_sub
## [1]  8 -2  2 -2
# c. multiply vectors (element-wise)
result_mul <- x * y
result_mul 
## [1] 20.00 35.00  5.25  8.00
# d. divide vectors (element-wise)
result_div <- x / y
result_div
## [1] 5.0000000 0.7142857 2.3333333 0.5000000
# e. element-wise modulo (remainder)
result_mod <- x %% y
result_mod
## [1] 0.0 5.0 0.5 2.0

Problem 3

Perform the following operations in R:

  1. Create a numeric vector x with 5 elements of your choice. (2 points)
  2. Compare each element of x to a threshold value (e.g., 5) using greater than (>) and less than (<) operators. Store the results in logical vectors. (8 points)
  3. Create two logical vectors L1 and L2, each with at least 5 elements, containing a mix of TRUE, FALSE, and NA values. (5 points)
  4. Create a mixed vector that demonstrates type coercion to numeric (for example, by combining numbers with logical values). Check its class and print the result. (5 points)
#Your code here

#create a numeric vector x with 5 elements

# a. create a numeric vector
x <- c(2, 7, 5, 10, 3)
x
## [1]  2  7  5 10  3
# b. Compare elements of x to 5
greater_than_5 <- x > 5 # TRUE  if element is greater than 5
less_than_5 <- x < 5 # TRUE if element is less than 5

greater_than_5
## [1] FALSE  TRUE FALSE  TRUE FALSE
less_than_5 
## [1]  TRUE FALSE FALSE FALSE  TRUE
# c. create logical vectors with TRUE, FALSE, and NA

L1 <- c(TRUE, FALSE, NA, TRUE, FALSE)
L2 <- c(FALSE, NA, TRUE, FALSE, TRUE)

# d. Mixed vector: numbers + logical values
mixed_vector <- c(1, 0, TRUE, FALSE, 5)

mixed_vector # Display the vector
## [1] 1 0 1 0 5
class(mixed_vector) #Check its class
## [1] "numeric"

Problem 4

Create two matrices in R and use cbind() and rbind() to combine them.

Instructions:
a. Create a 2 × 3 matrix A with numbers 1 through 6. (5 points)
b. Create another 2 × 3 matrix B with numbers 7 through 12. (5 points)
c. Use cbind(A, B) to combine the matrices by columns. (5 points)
d. Use rbind(A, B) to combine the matrices by rows. (5 points)

#Your code here

# a. create matrix A (2 rows, 3 columns)
A <- matrix(1:6, nrow = 2, ncol = 3, byrow = TRUE)
A
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
# b. Create matrix B (2 rows, 3 columns)
B <- matrix(7:12, nrow = 2, ncol = 3, byrow = TRUE)
B
##      [,1] [,2] [,3]
## [1,]    7    8    9
## [2,]   10   11   12
# c. combine A and B by columns
C_col <- cbind(A, B)
C_col
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    2    3    7    8    9
## [2,]    4    5    6   10   11   12
# d. Combine A and B by rows
C_row <- rbind(A, B)
C_row
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
## [3,]    7    8    9
## [4,]   10   11   12

Problem 5

Work with data frames and practice modifying row and column names.

Instructions:

  1. Create a data frame named students with the following columns:

    • Name = (“Alice”, “Bob”, “Charlie”)
    • Age = (20, 21, 19)
    • Grade = (“A”, “B”, “A”)
      (5 points)

  2. Print the data frame. (5 points)

  3. Change the row names of the data frame to "S1", "S2", "S3". (5 points)

  4. Change the column names of the data frame to "StudentName", "StudentAge", "StudentGrade". (5 points)

#Your code here

# a. Create a data frame with Name, Age, and Grade
students <- data.frame(
  Name = c("Alice", "Bob", "Charlie"),
  Age = c(20, 21, 19),
  Grade = c("A", "B", "A")
)

# b. Display the data frame
students
# c. Change row names to S1, S2, S3
rownames(students) <- c("S1", "S2", "S3")
students
# d. Change column names
colnames(students) <- c("StudentName", "StudentAge", "StudentGrade")
students