Correlation analysis in R Programming - Mini Project: Build & Apply

Correlation analysis

📖 Scenario: You are a data analyst working with a small dataset of students' study hours and their exam scores. You want to find out if there is a relationship between how much students study and how well they perform on the exam.

🎯 Goal: Build a simple R program that calculates the correlation between study hours and exam scores using the Pearson method.

📋 What You'll Learn

Create a data frame with exact columns and values

Create a variable for the correlation method

Calculate the correlation using the cor() function with the method variable

Print the correlation result

💡 Why This Matters

🌍 Real World

Correlation analysis helps understand relationships between variables, like study time and exam scores, which is useful in education, business, and science.

💼 Career

Data analysts and scientists use correlation to find patterns and insights in data that guide decisions and predictions.

1

Create the data frame

Create a data frame called students with two columns: study_hours and exam_scores. Use these exact values: study_hours = c(2, 3, 5, 6, 8) and exam_scores = c(50, 60, 75, 80, 90).

R Programming

# Create the data frame called students with study_hours and exam_scores
# Your code here

Hint

Use the data.frame() function to create the data frame with the exact column names and values.

2

Set the correlation method

Create a variable called method and set it to the string "pearson" to specify the correlation method.

R Programming

students <- data.frame(
  study_hours = c(2, 3, 5, 6, 8),
  exam_scores = c(50, 60, 75, 80, 90)
)
# Create the method variable and set it to "pearson"
# Your code here

Hint

Assign the string "pearson" to the variable method.

3

Calculate the correlation

Calculate the correlation between study_hours and exam_scores from the students data frame using the cor() function with the method variable. Store the result in a variable called correlation.

R Programming

students <- data.frame(
  study_hours = c(2, 3, 5, 6, 8),
  exam_scores = c(50, 60, 75, 80, 90)
)
method <- "pearson"
# Calculate the correlation and store it in correlation
# Your code here

Hint

Use cor() with the two columns and the method variable.

4

Print the correlation result

Print the value of the correlation variable using the print() function.

R Programming

students <- data.frame(
  study_hours = c(2, 3, 5, 6, 8),
  exam_scores = c(50, 60, 75, 80, 90)
)
method <- "pearson"
correlation <- cor(students$study_hours, students$exam_scores, method = method)
# Print the correlation
# Your code here

Hint

Use print(correlation) to show the correlation value.

Practice

1. What does the cor() function in R calculate?

easy

A. The correlation coefficient between two numeric vectors

B. The sum of two numeric vectors

C. The difference between two numeric vectors

D. The product of two numeric vectors

Solution

1. Step 1: Understand the purpose of cor()

   The cor() function is designed to calculate how two numeric vectors move together, which is called correlation.

2. Step 2: Identify the correct description

   Correlation coefficient measures the strength and direction of a linear relationship between two numeric vectors.

3. Final Answer:

   The correlation coefficient between two numeric vectors -> Option A

4. Quick Check:

   cor() calculates correlation [OK]

Hint: Remember: cor() finds how two numbers move together [OK]

Common Mistakes:

• Confusing correlation with sum or difference
• Thinking cor() calculates causation
• Using cor() on non-numeric data

2. Which of the following is the correct syntax to calculate correlation between vectors x and y in R?

easy

A. correlation_coefficient(x, y)

B. cor(x, y)

C. correlate(x, y)

D. correlation(x, y)

Solution

1. Step 1: Recall the R function name

   The correct function to calculate correlation in R is cor().

2. Step 2: Check the syntax

   The function takes two numeric vectors as arguments: cor(x, y).

3. Final Answer:

   cor(x, y) -> Option B

4. Quick Check:

   Use cor() with two vectors [OK]

Hint: Use exactly cor(x, y) to get correlation [OK]

Common Mistakes:

• Using incorrect function names like correlation()
• Adding extra arguments unnecessarily
• Using wrong argument order

3. What is the output of the following R code?

x <- c(1, 2, 3, 4, 5)
y <- c(2, 4, 6, 8, 10)
cor(x, y)

medium

A. 1

B. -1

C. 0

D. NA

Solution

1. Step 1: Analyze the vectors

   Vector y is exactly twice x for each element, so they have a perfect positive linear relationship.

2. Step 2: Calculate correlation

   Perfect positive linear relationship means correlation coefficient is 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   Perfect positive correlation = 1 [OK]

Hint: If one vector is a perfect multiple of another, cor = 1 [OK]

Common Mistakes:

• Confusing correlation with sum or mean
• Expecting 0 when vectors are related
• Misreading negative correlation

4. Identify the error in this R code for correlation:

x <- c(1, 2, 3)
y <- c(4, 5)
cor(x, y)

medium

A. cor() function is misspelled

B. Vectors contain non-numeric data

C. Vectors have different lengths causing an error

D. No error, code runs fine

Solution

1. Step 1: Check vector lengths

   Vector x has length 3, vector y has length 2, so lengths differ.

2. Step 2: Understand cor() requirements

   cor() requires vectors of equal length to compute correlation.

3. Final Answer:

   Vectors have different lengths causing an error -> Option C

4. Quick Check:

   cor() needs equal length vectors [OK]

Hint: Vectors must be same length for cor() [OK]

Common Mistakes:

• Ignoring vector length mismatch
• Assuming cor() auto-adjusts lengths
• Thinking cor() works with non-numeric data

5. You have two numeric vectors a and b with some missing values (NA). Which is the correct way to calculate correlation ignoring missing values in R?

hard

A. cor(a, b, removeNA = TRUE)

B. cor(a, b, na.rm = TRUE)

C. cor(a, b, method = "ignoreNA")

D. cor(a, b, use = "complete.obs")

Solution

1. Step 1: Understand handling of missing values in cor()

   The cor() function uses the use argument to specify how to handle missing values.

2. Step 2: Identify correct argument value

   Setting use = "complete.obs" tells R to use only pairs without any NA values.

3. Final Answer:

   cor(a, b, use = "complete.obs") -> Option D

4. Quick Check:

   Use use = "complete.obs" to ignore NA [OK]

Hint: Use use="complete.obs" to skip NA pairs [OK]

Common Mistakes:

• Using na.rm which is not an argument for cor()
• Using incorrect argument names like removeNA
• Assuming method argument handles NA