Question

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

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

Hours Spent Studying 0 2 3 4 6
Midterm Grades 63 66 81 84 93

Step 1 of 3: Calculate the coefficient of determination, R^2. Round your answer to three decimal places.

Step 2 of 3: Compute the mean square error (s2e) for the model. Round your answer to four decimal places.

Step 3 of 3: Compute the standard error (se) of the model. Round your answer to four decimal places.

Homework Answers

Answer #1
X Y (x-x̅)² (y-ȳ)² (x-x̅)(y-ȳ)
0 63 9.00 207.36 43.20
2 66 1.00 129.96 11.40
3 81 0.00 12.96 0.00
4 84 1.00 43.56 6.60
6 93 9.00 243.36 46.80
ΣX ΣY Σ(x-x̅)² Σ(y-ȳ)² Σ(x-x̅)(y-ȳ)
total sum 15 387 20 637.2 108.00
mean 3.00 77.40 SSxx SSyy SSxy

step 1)

R² =    (Sxy)²/(Sx.Sy) = 108²/(20*637.2) = 0.915

step 2)

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    54
      
mean square error =Se² =  SSE/(n-2) =    18.0000

step 3)

std error ,Se =    √(SSE/(n-2)) = √18 = 4.2426

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