To calculate the correlation coefficient (r) between the number of bids and the selling price, we use the Pearson correlation 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:

• $x$ represents the number of bids,
• $y$ represents the price in dollars,
• $n$ is the number of data points (5 in this case).

Let's compute this step by step using Python. numpy as np

Given data

price = np.array([110, 120, 150, 160, 190]) bids = np.array([11, 12, 14, 16, 19])

Calculate the correlation coefficient

r = np.corrcoef(bids, price)[0, 1]

Round to three decimal places

r_rounded = round(r, 3) r_roundedThe correlation coefficient $r$ is 0.990 (rounded to three decimal places). This indicates a very strong positive correlation between the number of bids and the item's selling price.

Would you like a breakdown of the calculations?

Here are five related questions to explore further:

1. What does a correlation coefficient of 0.990 imply in practical terms?
2. How do we interpret negative correlation coefficients?
3. What is the difference between correlation and causation?
4. How can we visualize this relationship using a scatter plot?
5. How does increasing the sample size affect correlation estimates?

Tip:

If $|r|$ is close to 1, it suggests a strong linear relationship, but it does not imply causation.