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	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.

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