Use the data values in the table below to calculate the correlation, r, between the variables x and y.
Hint: Use technology to do this...you do not need to compute this by hand.
x |
y |
1 |
17.98 |
2 |
21.56 |
3 |
25.84 |
4 |
27.72 |
5 |
27.4 |
6 |
29.18 |
7 |
33.56 |
8 |
32.44 |
9 |
35.82 |
Give your answer to rounded three decimal places.
Solution:
X | Y | XY | X^2 | Y^2 |
1 | 17.98 | 17.98 | 1 | 323.2804 |
2 | 21.56 | 43.12 | 4 | 464.8336 |
3 | 25.84 | 77.52 | 9 | 667.7056 |
4 | 27.72 | 110.88 | 16 | 768.3984 |
5 | 27.4 | 137 | 25 | 750.76 |
6 | 29.18 | 175.08 | 36 | 851.4724 |
7 | 33.56 | 234.92 | 49 | 1126.2736 |
8 | 32.44 | 259.52 | 64 | 1052.3536 |
9 | 35.82 | 322.38 | 81 | 1283.0724 |
n | 9 |
sum(XY) | 1378.40 |
sum(X) | 45.00 |
sum(Y) | 251.50 |
sum(X^2) | 285.00 |
sum(Y^2) | 7288.15 |
Numerator | 1088.10 |
Denominator | 1124.36 |
r | 0.9677 |
r square | 0.9365 |
Xbar(mean) | 5.0000 |
Ybar(mean) | 27.9444 |
SD(X) | 1.7078 |
SD(Y) | 3.9250 |
b | 2.0150 |
a | 17.8694 |
r = 0.968
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