To calculate the correlation coefficient $r$ for the given data, we can use the formula for the Pearson correlation coefficient:

$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{\left(n\sum x^2 - (\sum x)^2\right)\left(n\sum y^2 - (\sum y)^2\right)}}$

Where:

• $x$ is the number of bids,
• $y$ is the item's selling price in dollars,
• $n$ is the number of data points (which is 5 in this case).

We are given the following dataTo calculate the correlation coefficient $r$ for the given data, we can use the formula for the Pearson correlation coefficient:

$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{\left(n\sum x^2 - (\sum x)^2\right)\left(n\sum y^2 - (\sum y)^2\right)}}$

Where:

• $x$ is the number of bids,
• $y$ is the item's selling price in dollars,
• $n$ is the number of data points (which is 5 in this case).

We are given the following

$x = \{13, 14, 15, 18, 19\}$ $y = \{23, 35, 38, 41, 47\}$

Let's calculate the correlation coefficient step by step.

Step 1: Compute the necessary sums

$\sum x = 13 + 14 + 15 + 18 + 19 = 79$ $\sum y = 23 + 35 + 38 + 41 + 47 = 184$ $\sum x^2 = 13^2 + 14^2 + 15^2 + 18^2 + 19^2 = 169 + 196 + 225 + 324 + 361 = 1275$ $\sum y^2 = 23^2 + 35^2 + 38^2 + 41^2 + 47^2 = 529 + 1225 + 1444 + 1681 + 2209 = 7088$ $\sum xy = (13 \times 23) + (14 \times 35) + (15 \times 38) + (18 \times 41) + (19 \times 47)$ $\sum xy = 299 + 490 + 570 + 738 + 893 = 2990$

Step 2: Plug values into the correlation coefficient formula