Determine the Pearson product-moment correlation coefficient for the following data. x 1 10 9 6 4...
Determine the Pearson product-moment correlation coefficient for
the following data.
|
x |
1 | 10 | 9 | 6 | 4 | 3 | 2 |
|---|---|---|---|---|---|---|---|
|
y |
9 | 4 | 4 | 5 | 7 | 7 | 10 |
(Do not round the intermediate values. Round your
answer to 3 decimal places.)
Correlation coefficient, r
Homework Answers
Solution:
| X | Y | XY | X^2 | Y^2 |
| 1 | 9 | 9 | 1 | 81 |
| 10 | 4 | 40 | 100 | 16 |
| 9 | 4 | 36 | 81 | 16 |
| 6 | 5 | 30 | 36 | 25 |
| 4 | 7 | 28 | 16 | 49 |
| 3 | 7 | 21 | 9 | 49 |
| 2 | 10 | 20 | 4 | 100 |
| n | 8 |
| sum(XY) | 184.00 |
| sum(X) | 35.00 |
| sum(Y) | 46.00 |
| sum(X^2) | 247.00 |
| sum(Y^2) | 336.00 |
| Numerator | -322.00 |
| Denominator | 344.41 |
| r | -0.9337 |
| r square | 0.8717 |
| Xbar(mean) | 5.0000 |
| Ybar(mean) | 6.5714 |
| SD(X) | 3.2016 |
| SD(Y) | 1.8257 |
| b | -0.6389 |
| a | 9.7659 |
r = -0.934
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