Compute the Pearson Correlation coefficient for the following data (SSx= 10, and SSy= 10 )
X |
Y |
2 |
3 |
3 |
1 |
6 |
5 |
4 |
4 |
5 |
2 |
Solution;
X | Y | XY | X^2 | Y^2 |
2 | 3 | 6 | 4 | 9 |
3 | 1 | 3 | 9 | 1 |
6 | 5 | 30 | 36 | 25 |
4 | 4 | 16 | 16 | 16 |
5 | 2 | 10 | 25 | 4 |
n | 5 |
sum(XY) | 65.00 |
sum(X) | 20.00 |
sum(Y) | 15.00 |
sum(X^2) | 90.00 |
sum(Y^2) | 55.00 |
Numerator | 25.00 |
Denominator | 50.00 |
r | 0.5000 |
r square | 0.2500 |
Xbar(mean) | 4.0000 |
Ybar(mean) | 3.0000 |
SD(X) | 1.4142 |
SD(Y) | 1.4142 |
b | 0.5000 |
a | 1.0000 |
The Pearson Correlation coefficient is,
r = 0.5000
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