Question

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 26 29 32 38 47 Number of Bids 12 13 15 16 18 Step 3 of 3 : Calculate the correlation coefficient, r. Round your answer to three decimal places.\

Answer 1

Let's assume the following data:

Price in Dollars (X) 26 29 32 38 47

Number of Bids (Y) 12 13 15 16 18

For our case we have this:

n=10
`\sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118`

`r=(5(2623)-(172)(74))/(√([5(6194) -(172)^2][5(1118) -(74)^2]))=0.974`

So then the correlation coefficient would be r =0.974

Explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

And in order to calculate the correlation coefficient we can use this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

Let's assume the following data

Price in Dollars (X) 26 29 32 38 47

Number of Bids (Y) 12 13 15 16 18

For our case we have this:

n=10
`\sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118`

`r=(5(2623)-(172)(74))/(√([5(6194) -(172)^2][5(1118) -(74)^2]))=0.974`

So then the correlation coefficient would be r =0.974