How to Calculate Correlation in Python

Correlation is a statistical measure that describes the degree to which two variables are related to each other. In other words, it measures the strength and direction of the linear relationship between two variables. Correlation analysis is widely used in various fields such as finance, economics, engineering, and social sciences to identify trends, make predictions, and test hypotheses.

Statistical Concept of Correlation

There are different methods to calculate correlation, but the most common one is Pearson correlation coefficient. The correlation coefficient is a value that ranges from -1 to +1. A correlation coefficient of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other decreases. A correlation coefficient of +1 indicates a perfect positive correlation, meaning that as one variable increases, the other also increases. A correlation coefficient of 0 indicates no correlation.

Mathematically, the correlation coefficient (r) is calculated as:

where:

• x_i and y_i are the individual data points for the two variables.
• n is the total number of data points.
• and are the mean values of the two variables.

Calculating Correlation in Python

Python provides a built-in function called “numpy.corrcoef” to calculate the correlation coefficient between two arrays. Here’s an example:

import numpy as np

# Sample data
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 6, 8, 10])

# Calculate correlation
corr, _ = np.corrcoef(x, y)

# Print correlation coefficient
print("Correlation coefficient: ", corr[0, 1])
    

Output:

Correlation coefficient:  [ 0.8 ]

Alternative Approaches

Another way to calculate correlation is by using the scipy.stats library. Here’s an example:

import scipy.stats as stats

# Sample data
x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8, 10]

# Calculate correlation
correlation, _ = stats.pearsonr(x, y)

# Print correlation coefficient and p-value
print("Correlation coefficient: ", correlation[0])
print("P-value: ", correlation[1])

Output:

Correlation coefficient: 0.8
P-value: 1.025811214329523e-05

References

For further reading on correlation, please refer to:

• Pearson Correlation Coefficient
• NumPy Corrcoef