Correlation coefficient with np.corrcoef() in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.corrcoef() with simple arrays

What is the output of this code snippet?

import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
result = np.corrcoef(x, y)
print(result)

NumPy

import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
result = np.corrcoef(x, y)
print(result)

A

[[1. 1.]
 [1. 1.]]

B

[[1. 0.]
 [0. 1.]]

C

[[0. 1.]
 [1. 0.]]

D

[[1. -1.]
 [-1. 1.]]

💡 Hint

Think about how correlation measures linear relationship between two arrays.

The arrays x and y increase together perfectly, so their correlation coefficient is 1. The matrix shows correlation of each array with itself (1) and with the other (1).

❓ data_output

intermediate

Correlation matrix shape for multiple variables

Given three variables stored as arrays, what is the shape of the correlation matrix returned by np.corrcoef() when called as np.corrcoef(a, b, c)?

NumPy

import numpy as np
a = np.array([1, 2, 3])
b = np.array([3, 2, 1])
c = np.array([2, 2, 2])
result = np.corrcoef(a, b, c)
print(result.shape)

A (3,)

B (3, 3)

C (1, 3)

D (2, 2)

💡 Hint

The correlation matrix compares each variable with every other variable.

np.corrcoef returns a square matrix with size equal to the number of input variables, so 3 variables produce a 3x3 matrix.

🔧 Debug

advanced

Identify the error in np.corrcoef usage

What error will this code raise?

import numpy as np
x = [1, 2, 3]
y = [4, 5]
np.corrcoef(x, y)

NumPy

import numpy as np
x = [1, 2, 3]
y = [4, 5]
np.corrcoef(x, y)

A TypeError: unsupported operand type(s) for -: 'list' and 'list'

B No error, returns correlation matrix

C IndexError: index out of range

D ValueError: all the input arrays must have same length

💡 Hint

Think about the length of arrays passed to np.corrcoef.

np.corrcoef requires input arrays to have the same length to compute pairwise correlation. Different lengths cause a ValueError.

🚀 Application

advanced

Using np.corrcoef to find strongest correlation

You have three arrays representing different features. Which pair has the strongest positive correlation?

import numpy as np
f1 = np.array([1, 2, 3, 4])
f2 = np.array([4, 3, 2, 1])
f3 = np.array([2, 4, 6, 8])
cor_matrix = np.corrcoef(f1, f2, f3)
print(cor_matrix)

NumPy

import numpy as np
f1 = np.array([1, 2, 3, 4])
f2 = np.array([4, 3, 2, 1])
f3 = np.array([2, 4, 6, 8])
cor_matrix = np.corrcoef(f1, f2, f3)
print(cor_matrix)

A f1 and f3

B All pairs have equal correlation

C f2 and f3

D f1 and f2

💡 Hint

Look for pairs with correlation close to 1.

f1 and f3 increase together perfectly, so their correlation is 1. f1 and f2 are negatively correlated (-1).

🧠 Conceptual

expert

Interpretation of np.corrcoef output matrix

Given the correlation matrix below from np.corrcoef for variables A, B, and C:

[[ 1.   0.5 -0.3]
 [ 0.5  1.   0.1]
 [-0.3  0.1  1. ]]

Which statement is true?

A Variable B and C have a strong negative correlation.

B Variable A and C have a strong positive correlation.

C Variable A and B have a moderate positive correlation, and A and C have a weak negative correlation.

D All variables are uncorrelated.

💡 Hint

Correlation values near 0 mean weak correlation; near 1 or -1 mean strong.

0.5 is moderate positive correlation between A and B; -0.3 is weak negative correlation between A and C; 0.1 is very weak positive correlation between B and C.