Question
Annual high temperatures in a certain location have been tracked for several years. Let XX represent...
Annual high temperatures in a certain location have been tracked
for several years. Let XX represent the year and YY the high
temperature. Based on the data shown below, calculate the
correlation coefficient (to three decimal places) between XX and
YY. Use your calculator!
| x | y |
|---|---|
| 4 | 21.08 |
| 5 | 21.1 |
| 6 | 20.42 |
| 7 | 17.14 |
| 8 | 19.16 |
| 9 | 18.98 |
| 10 | 21 |
r=
Homework Answers
Answer #1
Solution:
| X | Y | XY | X^2 | Y^2 |
| 4 | 21.08 | 84.32 | 16 | 444.3664 |
| 5 | 21.1 | 105.5 | 25 | 445.21 |
| 6 | 20.42 | 122.52 | 36 | 416.9764 |
| 7 | 17.14 | 119.98 | 49 | 293.7796 |
| 8 | 19.16 | 153.28 | 64 | 367.1056 |
| 9 | 18.98 | 170.82 | 81 | 360.2404 |
| 10 | 21 | 210 | 100 | 441 |
| n | 7 |
| sum(XY) | 966.42 |
| sum(X) | 49.00 |
| sum(Y) | 138.88 |
| sum(X^2) | 371.00 |
| sum(Y^2) | 2768.68 |
| Numerator | -40.18 |
| Denominator | 135.08 |
| r | -0.2975 |
| r square | 0.0885 |
| Xbar(mean) | 7.0000 |
| Ybar(mean) | 19.8400 |
| SD(X) | 1.7078 |
| SD(Y) | 1.3982 |
| b | -0.2050 |
| a | 21.2750 |
r = -0.298
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