Vector arithmetic (element-wise) in R Programming - Mini Project: Build & Apply

Vector arithmetic (element-wise)

📖 Scenario: You are working with two sets of numbers representing daily temperatures in two different cities. You want to compare them by adding, subtracting, multiplying, and dividing the temperatures element by element.

🎯 Goal: Build a simple R program that creates two numeric vectors, sets a length variable, performs element-wise arithmetic operations on the vectors, and prints the results.

📋 What You'll Learn

Create two numeric vectors named city1_temps and city2_temps with exact values

Create a variable n that stores the length of the vectors

Use element-wise arithmetic operations: addition, subtraction, multiplication, and division

Print the results of each arithmetic operation

💡 Why This Matters

🌍 Real World

Element-wise vector arithmetic is useful when comparing or combining data points from two related datasets, like temperatures from two cities over several days.

💼 Career

Data analysts and scientists often use vector operations to quickly process and analyze numerical data without writing loops.

1

Create two numeric vectors

Create a numeric vector called city1_temps with values c(20, 22, 19, 24, 21) and another numeric vector called city2_temps with values c(18, 21, 20, 23, 22).

R Programming

# Create the vectors city1_temps and city2_temps with the exact values
# Your code here

Hint

Use the c() function to create vectors with the exact numbers given.

2

Create a length variable

Create a variable called n that stores the length of the vector city1_temps using the length() function.

R Programming

city1_temps <- c(20, 22, 19, 24, 21)
city2_temps <- c(18, 21, 20, 23, 22)
# Create variable n to store the length of city1_temps
# Your code here

Hint

Use length(city1_temps) to find how many elements are in the vector.

3

Perform element-wise arithmetic operations

Create four new vectors: sum_temps as the element-wise sum of city1_temps and city2_temps, diff_temps as the element-wise difference, prod_temps as the element-wise product, and quot_temps as the element-wise quotient.

R Programming

city1_temps <- c(20, 22, 19, 24, 21)
city2_temps <- c(18, 21, 20, 23, 22)
n <- length(city1_temps)
# Create sum_temps, diff_temps, prod_temps, and quot_temps using element-wise operations
# Your code here

Hint

Use +, -, *, and / operators directly on the vectors for element-wise operations.

4

Print the results

Print the vectors sum_temps, diff_temps, prod_temps, and quot_temps each on a separate line using the print() function.

R Programming

city1_temps <- c(20, 22, 19, 24, 21)
city2_temps <- c(18, 21, 20, 23, 22)
n <- length(city1_temps)
sum_temps <- city1_temps + city2_temps
diff_temps <- city1_temps - city2_temps
prod_temps <- city1_temps * city2_temps
quot_temps <- city1_temps / city2_temps
# Print sum_temps, diff_temps, prod_temps, and quot_temps
# Your code here

Hint

Use print() for each vector to see the results on separate lines.

Practice

1.

What happens when you add two vectors of the same length in R, like c(1, 2, 3) + c(4, 5, 6)?

easy

A. The vectors are concatenated into one longer vector.

B. Only the first elements are added, the rest are ignored.

C. Each element in the first vector is added to the corresponding element in the second vector.

D. An error occurs because vectors cannot be added.

Solution

1. Step 1: Understand element-wise addition

   In R, adding two vectors of the same length adds each element from the first vector to the matching element in the second vector.

2. Step 2: Apply addition to given vectors

   Adding c(1, 2, 3) and c(4, 5, 6) results in c(1+4, 2+5, 3+6) which is c(5, 7, 9).

3. Final Answer:

   Each element in the first vector is added to the corresponding element in the second vector. -> Option C

4. Quick Check:

   Element-wise addition = Each element in the first vector is added to the corresponding element in the second vector. [OK]

Hint: Add vectors element by element when lengths match [OK]

Common Mistakes:

• Thinking vectors concatenate instead of adding
• Assuming only first elements add
• Expecting an error for vector addition

2.

Which of the following is the correct syntax to subtract two vectors a and b element-wise in R?

easy

A. subtract_vectors(a, b)

B. subtract(a, b)

C. a %minus% b

D. a - b

Solution

1. Step 1: Recall vector subtraction syntax in R

   In R, element-wise subtraction of vectors uses the minus operator - directly between vectors.

2. Step 2: Verify given options

   Only a - b is valid R syntax for element-wise subtraction. The other options are not built-in R functions or operators.

3. Final Answer:

   a - b -> Option D

4. Quick Check:

   Use - operator for vector subtraction [OK]

Hint: Use '-' operator directly between vectors [OK]

Common Mistakes:

• Using non-existent functions like subtract()
• Trying special operators like %minus%
• Confusing subtraction with other functions

3.

What is the output of the following R code?

v1 <- c(2, 4, 6)
v2 <- c(1, 3, 5)
result <- v1 * v2
print(result)

medium

A. [1] 2 4 6 1 3 5

B. [1] 2 12 30

C. [1] 2 7 11

D. [1] 3 7 11

Solution

1. Step 1: Understand element-wise multiplication

   In R, multiplying two vectors multiplies each element of the first vector by the corresponding element of the second vector.

2. Step 2: Calculate each product

   Multiply elements: 2*1=2, 4*3=12, 6*5=30. So the result is c(2, 12, 30).

3. Final Answer:

   [1] 2 12 30 -> Option B

4. Quick Check:

   Element-wise multiplication = [1] 2 12 30 [OK]

Hint: Multiply vectors element by element for correct output [OK]

Common Mistakes:

• Adding instead of multiplying
• Concatenating vectors instead of multiplying
• Getting sums instead of products

4.

Consider this R code snippet:

v1 <- c(1, 2, 3)
v2 <- c(4, 5)
result <- v1 + v2
print(result)

What is the issue with this code?

medium

A. Vectors have different lengths causing recycling warning.

B. Syntax error due to missing operator.

C. Result will be NULL because vectors differ in length.

D. No issue; code runs correctly without warnings.

Solution

1. Step 1: Check vector lengths

   Vector v1 has length 3, v2 has length 2. They differ in length.

2. Step 2: Understand recycling in R

   R recycles the shorter vector to match the longer one but gives a warning if lengths are not multiples. Here, 3 is not a multiple of 2, so a warning occurs.

3. Final Answer:

   Vectors have different lengths causing recycling warning. -> Option A

4. Quick Check:

   Unequal vector lengths cause recycling warning [OK]

Hint: Vectors must be same length or multiples to avoid warnings [OK]

Common Mistakes:

• Ignoring recycling warnings
• Expecting syntax errors for length mismatch
• Assuming result is NULL when lengths differ

5.

You have two vectors representing daily sales for two stores:
store1 <- c(10, 20, 30, 40)
store2 <- c(5, 15, 25, 35)
How do you calculate the total sales per day for both stores combined using vector arithmetic?

hard

A. total_sales <- store1 + store2

B. total_sales <- store1 * store2

C. total_sales <- store1 - store2

D. total_sales <- c(store1, store2)

Solution

1. Step 1: Understand the goal

   We want total sales per day, so we add sales from both stores for each day.

2. Step 2: Use element-wise addition

   Adding store1 and store2 element-wise sums daily sales: c(10+5, 20+15, 30+25, 40+35) = c(15, 35, 55, 75).

3. Final Answer:

   total_sales <- store1 + store2 -> Option A

4. Quick Check:

   Add vectors element-wise for daily totals [OK]

Hint: Add vectors to combine daily sales totals [OK]

Common Mistakes:

• Multiplying instead of adding sales
• Subtracting sales mistakenly
• Concatenating vectors instead of adding