Question

Consider the data.

xi	1	2	3	4	5
yi	2	8	6	11	13

(a)

Compute the mean square error using equation  s² = MSE =

SSE

n − 2

 . (Round your answer to two decimal places.)

(b)

Compute the standard error of the estimate using equation s =

MSE

=

SSE n − 2

 . (Round your answer to three decimal places.)

(c)

Compute the estimated standard deviation of

b₁

using equation s_b1 =

s

Σ(xi − x)2

. (Round your answer to three decimal places.)

(d)

Use the t test to test the following hypotheses (α = 0.05):

H0:	β1	=	0
Ha:	β1	≠	0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We conclude that the relationship between x and y is significant. Reject H₀. We conclude that the relationship between x and y is significant.      Reject H₀. We cannot conclude that the relationship between x and y is significant. Do not reject H₀. We cannot conclude that the relationship between x and y is significant.

(e)

Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.

Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Regression
Error
Total

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =  

State your conclusion.

Reject H₀. We cannot conclude that the relationship between x and y is significant. Reject H₀. We conclude that the relationship between x and y is significant.      Do not reject H₀. We cannot conclude that the relationship between x and y is significant. Do not reject H₀. We conclude that the relationship between x and y is significant.

Answer 1

SSE =Syy-(Sxy)2/Sxx=

11.500

a)

s2 =SSE/(n-2)=

3.83

b)

std error σ              =

=se =√s2=

1.958

c)

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

0.619

d)

test stat t =	(bo-β1)/se(β1)=	=	4.038
p value:		=	0.0273

  Reject H₀. We conclude that the relationship between x and y is significant.

e)

Source	SS	df	MS	F	p value
regression	62.50	1	62.50	16.30	0.027
Residual error	11.50	3	3.83
Total	74.00	4

value of the test statistic =16.30

p value =0.027

Reject H₀. We conclude that the relationship between x and y is significant.