Question

Consider the data.

xi	1	2	3	4	5
yi	3	7	5	10	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.Do not 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.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 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.     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

Solution :

Data -----> Data Analysis -----> Regression ---->OK

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.914891
R Square	0.837025
Adjusted R Square	0.7827
Standard Error	1.852926
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	52.9	52.9	15.40777	0.029422
Error	3	10.3	3.433333
Total	4	63.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.7	1.943365	0.3602	0.742564	-5.48465	6.884654	-5.48465	6.884654
X Variable 1	2.3	0.585947	3.925273	0.029422	0.435257	4.164743	0.435257	4.164743

a)

From regression statistics,

s² = MSE = SSE / n - 2 = 10.3/ 5-2 = 13.9 / 3

s² = 3.43

b)

s = sqrt(MSE) = sqrt(SSE / n - 2) = sqrt(3.43)

s = 1.853

c)

d)

value of the test statistic

P value = 0.0294

Option C

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

e)

ANOVA
	df	SS	MS	F	F p value
Regression	1	52.9	52.9	15.41	0.029
Error	3	10.3	3.43
Total	4	63.2

the value of the test statistic = 15.41

P value = 0.029

Option A

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