The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams.
Hours Spent Studyin | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 4 | 4.5 | 6 |
---|---|---|---|---|---|---|---|---|---|---|
Midterm Grade | 66 | 72 | 78 | 81 | 84 | 87 | 90 | 93 | 96 | 99 |
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Step 3 of 3 :
Calculate the correlation coefficient, r. Round your answer to three decimal places.
X | Y | XY | X^2 | Y^2 |
0 | 66 | 0 | 0 | 4356 |
0.5 | 72 | 36 | 0.25 | 5184 |
1 | 78 | 78 | 1 | 6084 |
1.5 | 81 | 121.5 | 2.25 | 6561 |
2 | 84 | 168 | 4 | 7056 |
2.5 | 87 | 217.5 | 6.25 | 7569 |
3 | 90 | 270 | 9 | 8100 |
4 | 93 | 372 | 16 | 8649 |
4.5 | 96 | 432 | 20.25 | 9216 |
6 | 99 | 594 | 36 | 9801 |
n | 10 |
sum(XY) | 2289.00 |
sum(X) | 25.00 |
sum(Y) | 846.00 |
sum(X^2) | 95.00 |
sum(Y^2) | 72576.00 |
Numerator | 1740.00 |
Denominator | 1806.74 |
r | 0.9631 |
r square | 0.9275 |
Xbar(mean) | 2.5000 |
Ybar(mean) | 84.6000 |
SD(X) | 0.8539 |
SD(Y) | 7.1414 |
b | 5.3538 |
a | 71.2154 |
Step 3 of 3 :
Calculate the correlation coefficient = r = 0.963
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