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 23 29 32 38 41
Number of Birds 10 14 15 16 17
A) Step 1 of 3: Draw a scatter plot of the given data.

B)Step 2 of 3: Estimate the correlation in words: positive, negative, no correlation.

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

Answer 1

Answer:

Step 1: Figure attached

Step 2: Positive correlation

Step 3: r=0.9534

Step-by-step explanation:

Step 1

For this step we can use excel

We click on Insert> Insert Scatterpplot(X,Y) or Bubblechart. We select the data and then we select the Layout 9. Then we can edit the title and the names for the x and y axis.

The result obtained is on the Figure attached.

Step 2

As we can see on the plot obtained the slope obtained is positive since is increasing, so with this result we can conclude that the correlation would be positive and possible strong. We need to compute it in order to be sure of this.

Step 3

In order to calculate the correlation coefficient we can begin doing the following table:

n      x     y     xy        x*x       y*y

1     23    10   230    529     100

2     29    14   406    841     196

3     32    15    480    1024   225

4     38     16    608   1444    256

5     41      17     697   1681    289

$n =5 \sum x \sum y \sum xy \sum x^2 \sum y^2$

n=5 $\sum x = 163, \sum y = 72, \sum xy 2421, \sum x^2 =5519, \sum y^2 =1066$

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

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

$r=\frac{5(2421)-(163)(72)}{\sqrt{[5(5519) -(163)^2][5(1066) -(72)^2]}}=0.9534$

So then the correlation coefficient would be r =0.9534