Question

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

Hours Spent Studying	0	0.5	1.5	2.5	3	3.5	4	4.5	5	5.5
Grades	60	66	69	75	78	81	84	90	93	96

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Step 2 of 3:

Estimate the correlation in words: positive, negative, no correlation.

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

Answer 1

Solution:
From the data given in the question, we can say that the correlation between hours spent studying and grades are positive. because as hours spent studying increases than Grades also increases.
The correlation coefficient can be calculated as
Correlation coefficient =  ((n*Xi*Yi) - (Xi * Yi))/sqrt(((n*Xi^2) - (Xi)^2))*((n*Yi^2) - (Yi)^2)))

Hours Spent Studying(X)	Grades(Y)	X^2	Y^2	XY
0	60	0	3600	0
0.5	66	0.25	4356	33
1.5	69	2.25	4761	103.5
2.5	75	6.25	5625	187.5
3	78	9	6084	234
3.5	81	12.25	6561	283.5
4	84	16	7056	336
4.5	90	20.25	8100	405
5	93	25	8649	465
5.5	96	30.25	9216	528
30	792	121.5	64008	2575.5

Correlation coefficient = ((10*2575.5)-(30*72))/sqrt(((10*121.5)-(30*30))*((10*64008)-(792*792))) = 1995/sqrt(315*12816) = 0.993