Question

Consider the data.

xi	2	6	9	13	20
yi	5	16	8	24	23

(a)

What is the value of the standard error of the estimate? (Round your answer to three decimal places.)

(b)

Test for a significant relationship by using the t test. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₀ ≠ 0
H_a: β₀ = 0

H₀: β₁ ≠ 0
H_a: β₁ = 0    

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₀ = 0
H_a: β₀ ≠ 0

H₀: β₁ ≥ 0
H_a: 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 cannot conclude that the relationship between x and y is significant.

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

(c)

Use the F test to test for a significant relationship. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₁ ≥ 0
H_a: β₁ < 0    

H₀: β₀ = 0
H_a: β₀ ≠ 0

H₀: β₀ ≠ 0
H_a: β₀ = 0

H₀: β₁ ≠ 0
H_a: β₁ = 0

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 =

What is 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

Using Excel, go to Data, select Data Analysis, choose Regression.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.803
R Square	0.645
Adjusted R Square	0.526
Standard Error	5.910
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	190	190.000	5.439	0.1019
Residual	3	104.8	34.933
Total	4	294.8
	Coefficients	Standard Error	t Stat	P-value
Intercept	5.2	5.037	1.032	0.3778
X	1	0.429	2.332	0.1019

a) Standard error = 5.910

b) H₀: β₁ = 0
H_a: β₁ ≠ 0

Test statistic = 2.332

p-value = 0.1019

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

c) H₀: β₁ = 0
H_a: β₁ ≠ 0

Test statistic = 5.44

p-value = 0.102

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