Question

The following data gives the number of hours 10 students spent studying and their corresponding grades...

The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams.

Calculate the correlation coefficient, r. Round your answer to three decimal places.

Hours Spent Studying

 0.5 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Midterm Grades 63 66 69 72 75 81 84 90 96

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Math   Statistics-And-Probability   
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Answer #1

Solution:

X Y XY X^2 Y^2
0.5 63 31.5 0.25 3969
1.5 66 99 2.25 4356
2 69 138 4 4761
2.5 72 180 6.25 5184
3 75 225 9 5625
3.5 81 283.5 12.25 6561
4 84 336 16 7056
4.5 90 405 20.25 8100
5 96 480 25 9216
5.5 99 544.5 30.25 9801
n 10
sum(XY) 2722.50
sum(X) 32.00
sum(Y) 795.00
sum(X^2) 125.50
sum(Y^2) 64629.00
Numerator 1785.00
Denominator 1815.27
r 0.9833

Correlation coefficient r is given by

r = 0.983

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