Question

The following data gives the number of hours 5 students spent studying and their corresponding grades on their midterm exams.

Hours Spent Studying	0	1	2	4	5
Midterm Grades	69	72	75	84	93

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Step 1 of 3: Calculate the coefficient of determination, R2. Round your answer to three decimal places.

Step 2 of 3: Determine if r if statistically significant at the 0.01 level. (a) Yes (b) No

Step 3 of 3: Calculate the coefficient of determination, r^2. Round your answer to three decimal places.

Answer 1

Step 1 of 3:

Following are steps for calculating correlation coefficient (r):

Thus, r = 0.980

Step 2 of 3:

Test for significance of r:

The following needs to be tested:

H0​: ρ = 0 (Correlation coefficient is not significant)

HA​: ρ ≠ 0 (Correlation coefficient is significant)

where ρ corresponds to the population correlation.

Answer a) Yes, r is statistically significant at the 0.01 level

Step 3 of 3:

Coefficient of determination r² = 0.9804*0.9804 = 0.961