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.