Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5
 items sold through an auction.

Price in Dollars	23
35
38
41
47
Number of Bids	13
14
15
18
19

Step 3 of 3 :  Calculate the correlation coefficient, r. Round your answer to three decimal places.


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

Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction.
Price in Dollars: 23, 35, 38, 41, 47
Number of Bids: 13, 14, 15, 18, 19
Step 3 of 3: Calculate the correlation coefficient, r. Round your answer to three decimal places.

Learn how to calculate the Pearson correlation coefficient for eBay auction data using the number of bids and selling prices. This step-by-step solution includes sample data with 5 items and covers the core statistical concepts of correlation and linear relationships.

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