A study of bone density on 5 random women at a hospital produced the following results. Age 33 45 53 61 65 Bone Density 360 350 345 330 310
Step 3 of 3: Calculate the correlation coefficient, r. Round your answer to three decimal places.
Solution
| X | Y | XY | X^2 | Y^2 |
| 33 | 360 | 11880 | 1089 | 129600 |
| 45 | 350 | 15750 | 2025 | 122500 |
| 53 | 345 | 18285 | 2809 | 119025 |
| 61 | 330 | 20130 | 3721 | 108900 |
| 65 | 310 | 20150 | 4225 | 96100 |
| n | 5 |
| sum(XY) | 86195.00 |
| sum(X) | 257.00 |
| sum(Y) | 1695.00 |
| sum(X^2) | 13869.00 |
| sum(Y^2) | 576125.00 |
| Numerator | -4640.00 |
| Denominator | 5004.96 |
| r | -0.9271 |
| r square | 0.8595 |
| Xbar(mean) | 51.4000 |
| Ybar(mean) | 339.0000 |
| SD(X) | 11.4822 |
| SD(Y) | 17.4356 |
| b | -1.4078 |
| a | 411.3592 |
correlation coefficient, r = -0.927
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