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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 |
Solution
| S. 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 dr = 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(-3))/(sqrt(10xx203- (1)^2) xx sqrt(10xx159 -(-3)^2)`
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