To calculate the correlation coefficient ($r$), we use the formula:

[ r = \frac{n \sum xy - (\sum x)(\sum y)}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}} ]

Where:

• $x$ and $y$ are the data points in two variables.
• $n$ is the number of data pairs.

Given Data:

$x = [2.6, 4.6, 4.8, 3.7, 8.3, 5.2]$
$y = [14.7, 19.2, 18.5, 10.5, 19.7, 11.3]$

Let me calculate this for you.import numpy as np

Given data

x = np.array([2.6, 4.6, 4.8, 3.7, 8.3, 5.2]) y = np.array([14.7, 19.2, 18.5, 10.5, 19.7, 11.3])

Calculate correlation coefficient

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

Round to 2 decimal places

rounded_correlation_coefficient = round(correlation_coefficient, 2) rounded_correlation_coefficient0.50.5successThe correlation coefficient ($r$) is 0.50.

Would you like a detailed breakdown of the calculation? Let me know!

Here are five questions for further exploration:

1. What does the value of $r = 0.50$ indicate about the relationship between $x$ and $y$?
2. How does the correlation coefficient relate to causation?
3. Can we visualize the data points and the best-fit line for better understanding?
4. What would happen to $r$ if an outlier is introduced to the data?
5. How does the correlation coefficient change if all values of $x$ or $y$ are multiplied by a constant?

Tip: A correlation coefficient close to $0$ indicates weak linear dependence, while values closer to $1$ or $-1$ indicate strong positive or negative linear relationships.