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	20	26	41	44	47
Number of Bids	10	11	15	16	19

Step 3 of 3 :

Calculate the correlation coefficient, r. Round your answer to three decimal places

Answer 1

Solution:

Formula for correlation coefficient is given as below:

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

The required calculation table is given as below:

No.	x	y	x^2	y^2	xy
1	20	10	400	100	200
2	26	11	676	121	286
3	41	15	1681	225	615
4	44	16	1936	256	704
5	47	19	2209	361	893
Total	178	71	6902	1063	2698

∑x = 178

∑y = 71

∑x^2 = 6902

∑y^2 = 1063

∑xy = 2698

n = 5

r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

r = (5*2698 - 178*71)/sqrt[(5*6902– 178^2)*(5*1063 – 71^2)]

r = 852/ sqrt((5*6902- 178^2)*(5*1063 - 71^2))

r = 852/ 879.9568

r = 0.968229

Correlation coefficient = r = 0.968