Correlation analysis in R Programming - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate Pearson correlation coefficient

What is the output of this R code snippet that calculates the Pearson correlation between two numeric vectors?

R Programming

x <- c(1, 2, 3, 4, 5)
y <- c(2, 4, 6, 8, 10)
correlation <- cor(x, y, method = "pearson")
print(round(correlation, 2))

A 0.5

B 0

C -1

D 1

💡 Hint

Pearson correlation measures linear relationship strength between two variables.

The vectors x and y have a perfect positive linear relationship (y is exactly 2 times x), so the Pearson correlation is 1.

❓ Predict Output

intermediate

Spearman correlation with tied ranks

What is the output of this R code that calculates Spearman correlation for vectors with tied values?

R Programming

a <- c(1, 2, 2, 3, 4)
b <- c(5, 6, 6, 7, 8)
result <- cor(a, b, method = "spearman")
print(round(result, 2))

A 1

B 0.9

C 0.7

D 0.5

💡 Hint

Spearman correlation uses ranks and handles ties by averaging ranks.

Despite ties, the ranks of a and b perfectly correspond, so Spearman correlation is 1.

❓ Predict Output

advanced

Correlation matrix with NA values

What is the output of this R code that computes correlation matrix with missing values?

R Programming

data <- data.frame(
  v1 = c(1, 2, NA, 4),
  v2 = c(2, NA, 6, 8),
  v3 = c(5, 6, 7, 8)
)
result <- cor(data, use = "complete.obs")
print(round(result, 2))

A

[[1,1]] 1, [[1,2]] 0.98, [[1,3]] 0.99
[[2,1]] 0.98, [[2,2]] 1, [[2,3]] 0.98
[[3,1]] 0.99, [[3,2]] 0.98, [[3,3]] 1

B

[[1,1]] 1, [[1,2]] 0.99, [[1,3]] 1
[[2,1]] 0.99, [[2,2]] 1, [[2,3]] 0.99
[[3,1]] 1, [[3,2]] 0.99, [[3,3]] 1

C

[[1,1]] 1, [[1,2]] NA, [[1,3]] 1
[[2,1]] NA, [[2,2]] 1, [[2,3]] NA
[[3,1]] 1, [[3,2]] NA, [[3,3]] 1

D

[[1,1]] 1, [[1,2]] 1, [[1,3]] 1
[[2,1]] 1, [[2,2]] 1, [[2,3]] 1
[[3,1]] 1, [[3,2]] 1, [[3,3]] 1

💡 Hint

Using 'complete.obs' excludes rows with any NA in any variable pair.

Only rows without any NA in the pair are used for each correlation. The resulting matrix has values close to 1 but less than 1 due to fewer data points.

❓ Predict Output

advanced

Partial correlation calculation

What is the output of this R code that calculates the partial correlation between x and y controlling for z?

R Programming

library(ppcor)
x <- c(1, 2, 3, 4, 5)
y <- c(2, 1, 4, 3, 5)
z <- c(5, 4, 3, 2, 1)
result <- pcor.test(x, y, z)
print(round(result$estimate, 2))

A -0.9

B -0.4

C 0.0

D 0.8

💡 Hint

Partial correlation measures relationship between x and y after removing effect of z.

The partial correlation is negative because controlling for z reverses the apparent positive association between x and y.

🧠 Conceptual

expert

Interpreting correlation significance test output

Given this R output from cor.test(x, y), which statement correctly interprets the p-value and correlation estimate?

R Programming

x <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
y <- c(2, 1, 4, 3, 5, 7, 6, 8, 9, 10)
test <- cor.test(x, y)
print(test$p.value)
print(round(test$estimate, 2))

A The correlation is about 0.03 and is statistically significant at 0.05 level.

B The correlation is about 0.97 but not statistically significant at 0.05 level.

C The correlation is about 0.97 and is statistically significant at 0.05 level.

D The correlation is about 0.03 and not statistically significant at 0.05 level.

💡 Hint

Check both the correlation estimate and the p-value to interpret significance.

The correlation estimate is close to 0.97, indicating strong positive correlation, and the p-value is very small, so it is statistically significant.

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