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?
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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