Question

Calculate the Karl Pearson Correlation Co-efficient for the following data:

Demand for Product X:	23	27	28	29	30	31	33	35	36	39
Sale of Product Y:	18	22	23	24	25	26	28	29	30	32

Answer 1

Sr. No.	X	Y	(X-A) = dx	(Y-A) = dy	dx2	dy2	dxdy
1	23	18	−8	−8	64	64	64
2	27	22	−4	−4	16	16	16
3	28	23	−3	−3	9	9	9
4	29	24	−2	−2	4	4	4
5	30	25	−1	−1	1	1	1
6	31	26	0	0	0	0	0
7	33	28	2	2	4	4	4
8	35	29	4	3	16	9	12
9	36	30	5	4	25	16	20
10	39	32	8	6	64	36	48
N = 10	∑X = 311	∑Y = 257	∑(X−A) = 1	∑(Y-A) = (−2)	∑dx2 = 203	∑dy2 = 159	∑dxdy = 178

`barx = (sumX)/N = 311/10 = 31.1`

`barx = (sumY)/N = 257/10 = 25.7`

Take the assumed values A = 31 and B = 26

Therefore

dx = X − A ⇒ X − 31 and

dy = Y − A ⇒ Y − 26

`∴ r = (Nsumdxdy - (sumdx)(sumdy))/(sqrt(Nsumdx^2-(sumdx)^2)sqrt(Nsumdy^2-(sumdy)^2)`

`= (10xx178 -1xx(-2))/(sqrt(10xx203- (1)^2) xx sqrt(10xx159 -(-3)^2)`

= `r = (1780 + 2)/(sqrt(2030 - 1) * sqrt(1590 - 4)) = (1782)/(sqrt(2029*1586))`

= `r = (1782)/(sqrt(3219494)) = (1782)/(1793.17)`

r ≈ 0.9955