Read the table below:
X | Y |
13 | 18 |
14 | 21 |
17 | 19 |
11 | 20 |
12 | 16 |
10 | 13 |
Determine
1. the correlation coefficient (r)
2. The coefficient of determination (r 2)
Solution:
X | Y | XY | X^2 | Y^2 |
13 | 18 | 234 | 169 | 324 |
14 | 21 | 294 | 196 | 441 |
17 | 19 | 323 | 289 | 361 |
11 | 20 | 220 | 121 | 400 |
12 | 16 | 192 | 144 | 256 |
10 | 13 | 130 | 100 | 169 |
n | 6 |
sum(XY) | 1393.00 |
sum(X) | 77.00 |
sum(Y) | 107.00 |
sum(X^2) | 1019.00 |
sum(Y^2) | 1951.00 |
Numerator | 119.00 |
Denominator | 218.05 |
r | 0.5458 |
r square | 0.2978 |
Xbar(mean) | 12.8333 |
Ybar(mean) | 17.8333 |
SD(X) | 2.2669 |
SD(Y) | 2.6719 |
b | 0.6432 |
a | 9.5784 |
r = 0.546
r2 = 0.298
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