To calculate the correlation coefficient $r$ between the number of bids and the item's 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 (in this case, $n = 5$)

We will now compute the values for:

• $\sum x$, $\sum y$, $\sum xy$, $\sum x^2$, and $\sum y^2$.

Let's calculate. Given data x = [11, 12, 14, 16, 19] # Number of bids y = [110, 120, 150, 160, 190] # Price in dollars

Compute necessary sums

n = len(x) sum_x = sum(x) sum_y = sum(y) sum_x2 = sum(xi2 for xi in x) sum_y2 = sum(yi2 for yi in y) sum_xy = sum(x[i] * y[i] for i in range(n))

Compute correlation coefficient r

numerator = (n * sum_xy) - (sum_x * sum_y) denominator = ((n * sum_x2 - sum_x2) * (n * sum_y2 - sum_y2)) ** 0.5 r = numerator / denominator

Round to three decimal places

round(r, 3)The 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 selling price.

Would you like a step-by-step breakdown of the calculation?

Related Questions:

1. What does a correlation coefficient of 0.990 imply in practical terms?
2. How can we interpret the strength and direction of a correlation coefficient?
3. What is the coefficient of determination ($r^2$) and how is it useful?
4. How would adding more data points affect the correlation?
5. What other statistical methods can be used to analyze auction data?

Tip: A correlation close to 1 means that as one variable increases, the other also increases in a nearly linear fashion!