Determine the value of the coefficient of correlation,
r, for the following data.
| X | 2 | 6 | 7 | 11 | 16 | 17 | 21 |
| Y | 18 | 15 | 13 | 8 | 7 | 7 | 6 |
(Round the intermediate values to 3 decimal places.
Round your answer to 3 decimal places.)
r =
Solution:
| X | Y | XY | X^2 | Y^2 |
| 2 | 18 | 36 | 4 | 324 |
| 6 | 15 | 90 | 36 | 225 |
| 7 | 13 | 91 | 49 | 169 |
| 11 | 8 | 88 | 121 | 64 |
| 16 | 7 | 112 | 256 | 49 |
| 17 | 7 | 119 | 289 | 49 |
| 21 | 6 | 126 | 441 | 36 |
| n | 7 |
| sum(XY) | 662.00 |
| sum(X) | 80.00 |
| sum(Y) | 74.00 |
| sum(X^2) | 1196.00 |
| sum(Y^2) | 916.00 |
| Numerator | -1286.00 |
| Denominator | 1358.60 |
| r | -0.9466 |
| r square | 0.8960 |
| Xbar(mean) | 11.4286 |
| Ybar(mean) | 10.5714 |
| SD(X) | 5.3980 |
| SD(Y) | 4.2687 |
| b | -0.6521 |
| a | 18.0243 |

r = -0.947
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