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Question
Find the coefficient of correlation for the following data:
| X | 35 | 40 | 60 | 79 | 83 | 95 |
| Y | 17 | 28 | 30 | 32 | 38 | 49 |
Solution
| X | Y | dx = X − 65 | dy = Y − 32 | dx2 | dy2 | dxdy |
| 35 | 17 | − 30 | − 15 | 900 | 225 | 450 |
| 40 | 28 | − 25 | − 4 | 625 | 16 | 100 |
| 60 | 30 | − 5 | − 2 | 25 | 4 | 10 |
| 79 | 32 | 14 | 0 | 196 | 0 | 0 |
| 83 | 38 | 18 | 6 | 324 | 36 | 108 |
| 95 | 49 | 30 | 17 | 900 | 289 | 510 |
| 392 | 194 | 2 | 2 | 2970 | 570 | 1178 |
`bar"X" = 392/6` = 65.33
`bar"Y" = 194/6` = 32.33
Coefficient of correlation
r(X, Y) = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/(sqrt("N"sum"dx"^2 - (sum"dx")^2) xx sqrt("N"sum"dy"^2 - (sum"dy")^2))`
= `(6(1178) - 2(2))/(sqrt(6(2970) - 4) xx sqrt(6(570) - 4))`
= `7064/(sqrt17816 xx sqrt3416)`
= `7065/((133.48) (58.45))`
= `7064/7801.91`
= 0.906
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