Question

Given are five observations collected in a regression study on two variables.

x i	2	6	9	13	20
y i	7	18	9	26	23

1. Compute SSE, SST, and SSR (round to one decimals).

2. Compute the coefficient of determination (round to four decimals).

3. Compute the mean square error (round to two decimals).

4. Compute the estimated standard deviation of b₁ (round to four decimals).

5. Compute the p-value and t value (test statistic) of the t test to test the following hypotheses (round to three decimals)

H₀: β 1 = 0 and Ha: β 1 ≠ 0.

6. Compute the p-value and F value (test statistic) of the F test to test the following hypotheses (round to two decimals):

H₀: β 1 = 0 and Ha: β 1 ≠ 0.

Answer 1

1)

SSE =Syy-(Sxy)2/Sxx=

127.3

SST=Syy=

281.2

SSR =(Sxy)2/Sxx =

153.9

2)

Coeffficient of determination R^2 =SSR/SST=

0.5473

3)

MSE =

s2 =SSE/(n-2)=

42.43

4)

estimated std error of slope =se(β1) =s/√Sxx=

0.4726

5)

test stat t =	(bo-β1)/se(β1)=	=	1.904
p value:		=	0.1530

6)

Source	SS	df	MS	F	p value
regression	153.900	1	153.900	3.627	0.153
Residual error	127.300	3	42.433
Total	281.200	4

test statistic F =3.63

p value =0.1530