Question
0.9. Compute and interpret the correlation coefficient for the following grades of 6 students selected at...
0.9. Compute and interpret the correlation coefficient for the following grades of 6 students
selected at random.
| Mathematical Grade | 70 | 92 | 80 | 74 | 65 | 83 |
| English Grade | 74 | 84 | 63 | 87 | 78 | 90 |
Homework Answers
Answer #1
Solution:
From the data,
| X | Y | XY | X^2 | Y^2 |
| 70 | 74 | 5180 | 4900 | 5476 |
| 92 | 84 | 7728 | 8464 | 7056 |
| 80 | 63 | 5040 | 6400 | 3969 |
| 74 | 87 | 6438 | 5476 | 7569 |
| 65 | 78 | 5070 | 4225 | 6084 |
| 83 | 90 | 7470 | 6889 | 8100 |
| n | 6 |
| sum(XY) | 36926.00 |
| sum(X) | 464.00 |
| sum(Y) | 476.00 |
| sum(X^2) | 36354.00 |
| sum(Y^2) | 38254.00 |
| Numerator | 692.00 |
| Denominator | 2887.38 |
| r | 0.2397 |
| r square | 0.0574 |
| Xbar(mean) | 77.3333 |
| Ybar(mean) | 79.3333 |
| SD(X) | 8.8632 |
| SD(Y) | 9.0492 |
| b | 0.2447 |
| a | 60.4102 |
The correlation coefficient = r = 0.2397
A perfect positive relationship correlation coefficient is 0.2397, A fairly strong positive relationship.
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