Question
Questions 2-7 will all be in regards to this data set: Observation X Y 1 20...
Questions 2-7 will all be in regards to this data set:
| Observation | X | Y |
| 1 | 20 | 30 |
| 2 | 23 | 35 |
| 3 | 28 | 40 |
| 4 | 26 | 38 |
| 5 | 24 | 37 |
| 6 | 32 | 45 |
| 7 | 35 | 50 |
| 8 | 24 | 34 |
| 9 | 31 | 42 |
| 10 | 23 | 32 |
What is the Pearson's coefficient of correlation for the data set above?
Homework Answers
Answer #1
The statistic software output for this problem is:
| X | Y | XY | X^2 | Y^2 |
| 20 | 30 | 600 | 400 | 900 |
| 23 | 35 | 805 | 529 | 1225 |
| 28 | 40 | 1120 | 784 | 1600 |
| 26 | 38 | 988 | 676 | 1444 |
| 24 | 37 | 888 | 576 | 1369 |
| 32 | 45 | 1440 | 1024 | 2025 |
| 35 | 50 | 1750 | 1225 | 2500 |
| 24 | 34 | 816 | 576 | 1156 |
| 31 | 42 | 1302 | 961 | 1764 |
| 23 | 32 | 736 | 529 | 1024 |
| n | 10 |
| sum(XY) | 10445.00 |
| sum(X) | 266.00 |
| sum(Y) | 383.00 |
| sum(X^2) | 7280.00 |
| sum(Y^2) | 15007.00 |
| Numerator | 2572.00 |
| Denominator | 2628.83 |
| r | 0.9784 |
| r square | 0.9572 |
| Xbar(mean) | 26.6000 |
| Ybar(mean) | 38.3000 |
| SD(X) | 3.8188 |
| SD(Y) | 4.5735 |
| b | 1.2583 |
| a | 4.8288 |
the Pearson's coefficient of correlation = 0.9784
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