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Question
Calculate the correlation coefficient for the following data.
| X | 25 | 18 | 21 | 24 | 27 | 30 | 36 | 39 | 42 | 48 |
| Y | 26 | 35 | 48 | 28 | 20 | 36 | 25 | 40 | 43 | 39 |
Solution
| X | Y | x = `"X" - bar"X"` | y = `"Y" - bar"Y"` | x2 | y2 | xy |
| 25 | 26 | 6 | − 8 | 36 | 64 | 48 |
| 18 | 35 | − 13 | 1 | 169 | 1 | − 13 |
| 21 | 48 | − 10 | 14 | 100 | 196 | − 140 |
| 24 | 28 | − 7 | − 6 | 49 | 36 | 42 |
| 27 | 20 | − 4 | − 14 | 16 | 196 | 56 |
| 30 | 36 | − 1 | 2 | 1 | 4 | − 2 |
| 36 | 25 | 5 | − 9 | 25 | 81 | − 45 |
| 39 | 40 | 8 | 6 | 64 | 36 | 48 |
| 42 | 43 | 11 | 9 | 121 | 81 | 99 |
| 45 | 39 | 17 | 5 | 289 | 25 | 85 |
| 310 | 340 | 0 | 0 | 870 | 720 | 178 |
N = 10, ΣX = 310, ΣY = 340, Σx2 = 870, Σy2 = 720, Σxy = 178
`bar"X" = (sum"X")/"N" = 310/10` = 31
`bar"Y" = (sum"Y")/"N" = 340/10` = 34
Correlation coefficient
r = `(sum"xy")/sqrt(sum"x"^2 sum"y"^2)`
= `178/sqrt(870 xx 720)`
= `178/791.5`
= 0.225
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