Compute the linear correlation coefficient from the given table.
X |
1 |
2 |
4 |
6 |
7 |
|
Y |
10 |
11 |
9 |
6 |
4 |
Solution:
X | Y | XY | X^2 | Y^2 |
1 | 10 | 10 | 1 | 100 |
2 | 11 | 22 | 4 | 121 |
4 | 9 | 36 | 16 | 81 |
6 | 6 | 36 | 36 | 36 |
7 | 4 | 28 | 49 | 16 |
n | 5 |
sum(XY) | 132.00 |
sum(X) | 20.00 |
sum(Y) | 40.00 |
sum(X^2) | 106.00 |
sum(Y^2) | 354.00 |
Numerator | -140.00 |
Denominator | 148.66 |
r | -0.9417 |
r square | 0.8869 |
Xbar(mean) | 4.0000 |
Ybar(mean) | 8.0000 |
SD(X) | 2.2804 |
SD(Y) | 2.6077 |
b | -1.0769 |
a | 12.3077 |
r = -0.942
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