import numpy as np

Given data

x = np.array([4, 6, 9, 12, 15, 18, 20]) y = np.array([48.9, 85.1, 71.3, 64.9, 90.7, 55.3, 25.3])

Calculating the correlation coefficient

r = np.corrcoef(x, y)[0, 1]

Rounding the result to the nearest thousandth

r_rounded = round(r, 3) r_rounded-0.382-0.382successThe correlation coefficient $r$ is approximately equal to $-0.382$.

Would you like me to explain the process in detail or provide further insights? Here are some additional related questions for exploration:

1. What does a negative correlation coefficient imply about the relationship between $x$ and $y$?
2. How would removing one data point affect the correlation coefficient?
3. Can the correlation coefficient determine causation between $x$ and $y$?
4. How would the correlation coefficient change if all $y$-values were scaled by a constant factor?
5. What is the difference between correlation and regression analysis?

Tip: The closer the correlation coefficient is to $-1$ or $1$, the stronger the linear relationship.