import numpy as np from scipy.stats import pearsonr

Given bivariate data set

x = np.array([26.8, 22.1, 40.5, 7.1, 34.8, 42, 25.7, 24.9, 30.8, 15.9, 47.9, 17.9]) y = np.array([81.2, -38.9, 106.5, 14.9, 76.4, 104.6, 85.9, 59.6, 109.8, 88.8, 62.3, 30])

Calculating the Pearson correlation coefficient

correlation_coefficient, _ = pearsonr(x, y) correlation_coefficient0.50654882056840030.5065488205684003successThe correlation coefficient $r$ is 0.507 (accurate to three decimal places).

Would you like details or have any questions?

1. How is the correlation coefficient interpreted in statistics?
2. What does a positive correlation like this signify about the data?
3. What is the difference between Pearson and Spearman correlation?
4. How does sample size impact the reliability of the correlation coefficient?
5. Can correlation imply causation? Why or why not?

Tip: Always visualize your data (e.g., scatter plot) to better understand correlation patterns!