Pearson correlation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate Pearson correlation coefficient

What is the output of this code that calculates the Pearson correlation coefficient between two lists?

SciPy

from scipy.stats import pearsonr
x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8, 10]
result = pearsonr(x, y)
print(round(result[0], 2))

A 1.00

B 0.00

C -1.00

D 0.50

💡 Hint

Pearson correlation measures linear relationship strength between two variables.

The lists x and y have a perfect positive linear relationship (y is exactly 2 times x). So, the Pearson correlation coefficient is 1.00.

❓ data_output

intermediate

Number of pairs with strong positive correlation

Given this DataFrame, how many pairs of columns have a Pearson correlation coefficient greater than 0.8?

SciPy

import pandas as pd
import numpy as np
np.random.seed(0)
data = pd.DataFrame({
  'A': np.random.rand(10),
  'B': np.random.rand(10),
  'C': np.linspace(0, 1, 10),
  'D': np.linspace(0, 1, 10) * 2
})
corr_matrix = data.corr()
strong_pairs = (corr_matrix.where(np.triu(np.ones(corr_matrix.shape), k=1).astype(bool)) > 0.8).sum().sum()
print(int(strong_pairs))

A 2

B 0

C 3

D 1

💡 Hint

Check pairs only once and ignore diagonal.

Columns C and D are perfectly correlated (correlation 1). A and B have low correlation (~ -0.03), and other cross pairs are also low. The upper triangular mask counts unique off-diagonal pairs once, so only 1 pair (C, D).

🔧 Debug

advanced

Identify the error in Pearson correlation calculation

What error does this code raise when trying to calculate Pearson correlation?

SciPy

from scipy.stats import pearsonr
x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8]
pearsonr(x, y)

A IndexError: list index out of range

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

C ValueError: x and y must have the same length

D No error, returns correlation

💡 Hint

Check if both lists have the same number of elements.

The lists x and y have different lengths (5 and 4). pearsonr requires equal length inputs and raises ValueError if lengths differ.

🚀 Application

advanced

Interpret Pearson correlation result

If the Pearson correlation coefficient between two variables is -0.85, what does this mean?

A Strong negative linear relationship

B Perfect positive linear relationship

C No linear relationship

D Strong positive linear relationship

💡 Hint

Negative values indicate inverse relationships.

A correlation of -0.85 means a strong negative linear relationship: as one variable increases, the other tends to decrease.

🧠 Conceptual

expert

Effect of outliers on Pearson correlation

Which statement best describes how outliers affect the Pearson correlation coefficient?

A Outliers always increase the Pearson correlation value

B Outliers can greatly distort the Pearson correlation, making it unreliable

C Outliers have little to no effect on Pearson correlation

D Outliers convert Pearson correlation into a non-linear measure

💡 Hint

Think about how extreme values influence averages and covariance.

Pearson correlation is sensitive to outliers because it uses means and standard deviations. Extreme values can skew the correlation, making it misleading.