Question
The following data gives the number of hours 55 students spent studying and their corresponding grades...
The following data gives the number of hours 55 students spent studying and their corresponding grades on their midterm exams.
| Hours Spent Studying | 00 | 11 | 22 | 44 | 55 |
|---|---|---|---|---|---|
| Midterm Grades | 66 | 75 | 84 | 87 | 90 |
Copy Data
Calculate the coefficient of determination, R2. Round your answer to three decimal places.
Homework Answers
Answer #1
Solution:
| Hours spent studying(X) | Midterm Grades(Y) | XBAR | YBAR | X-XBAR | Y-YBAR | (X-XBAR)(Y-YBAR) | (X-XBAR)^2 | (Y-YBR)^2 | |
| 0 | 66 | 26.4 | 80.4 | -26.4 | -14.4 | 380.16 | 696.96 | 207.36 | |
| 11 | 75 | 26.4 | 80.4 | -15.4 | -5.4 | 83.16 | 237.16 | 29.16 | |
| 22 | 84 | 26.4 | 80.4 | -4.4 | 3.6 | -15.84 | 19.36 | 12.96 | |
| 44 | 87 | 26.4 | 80.4 | 17.6 | 6.6 | 116.16 | 309.76 | 43.56 | |
| 55 | 90 | 26.4 | 80.4 | 28.6 | 9.6 | 274.56 | 817.96 | 92.16 | |
| MEAN=132/5=26.4 | MEAN=402/5=80.4 | TOTAL | 838.2 | 2081.2 | 385.2 | ||||
r=
r=838.2/sqrt(2081.2*385.2)
=0.93615
coefficient of determination=r sq=r*r=0.93615*0.93615=0.8763768
r sq=0.876
he coefficient of determination, R2.=0.876
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