python covariance matrix
import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns Example 1 Manual
stock_a = [100, 102, 104, 103, 105] stock_b = [200, 198, 202, 204, 206] n = len(stock_a) # Step 1: Calculate the means of stock_a and stock_b mean_a = sum(stock_a) / n mean_b = sum(stock_b) / n # Step 2: Calculate the differences from the means and their products diff_product_sum = 0 for i in range(n): diff_a = stock_a[i] - mean_a diff_b = stock_b[i] - mean_b diff_product_sum += diff_a * diff_b # Step 3: Calculate the covariance covariance = diff_product_sum / n print(covariance) 
#The positive value of 3.6 indicates that the prices of Stock A and Stock B tend to move in the same
#direction. When the price of Stock A increases, the price of Stock B also tends to increase,
#and vice versa.
Example 2 Numpy Sample Covariance
X = [2.1, 2.5, 3.6, 4.0] Y = [8, 10, 12, 14] cov_matrix = np.cov(X, Y) print("Covariance matrix:\n", cov_matrix) 
cov_xy = cov_matrix[0, 1] print("Covariance between X and Y:", cov_xy) 
Example 4 Pandas Sample - No Option
data = {'X': [2.1, 2.5, 3.6, 4.0], 'Y': [8, 10, 12, 14]} df = pd.DataFrame(data) cov_df = df.cov() print("Covariance DataFrame:\n", cov_df) 
cov_xy = cov_df.loc['X', 'Y'] print("Covariance between X and Y:", cov_xy) 
Example 5 Plot Covariance Matrix
# Plot the covariance matrix as a heatmap plt.figure(figsize=(8, 6)) sns.heatmap(cov_matrix, annot=True, cmap='coolwarm', fmt='.2f') plt.title('Covariance Matrix') plt.show() 
plt.scatter(X, Y) plt.xlabel('X') plt.ylabel('Y') plt.title('Scatter plot of X vs Y') plt.show() 
