Question

Consider the data.

xi	2	6	9	13	20
yi	7	19	8	24	22

(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: β₁ ≠ 0
H_a: β₁ = 0

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

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 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.

(c)

Use the F test to test for a significant relationship. 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: β₀ ≠ 0
H_a: β₀ = 0

H₀: β₁ ≠ 0
H_a: β₁ = 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 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.

Answer 1

Solution:

We can use the excel regression data analysis tool to find the answer to the given questions. The excel steps are:

Enter the data in excel.

Click on Data > Data analysis > Regression > Ok

Input Y range: Select all the data under yi including label

Input X range: Select all the data under xi including label

Mark the labels

Choose the output range and the output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6919
R Square	0.4787
Adjusted R Square	0.3050
Standard Error	6.6433
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	121.6	121.6000	2.7553	0.1955
Residual	3	132.4	44.1333
Total	4	254
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8	5.6617	1.4130	0.2525	-10.0180	26.0180
xi	0.8	0.4820	1.6599	0.1955	-0.7338	2.3338

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

Answer:

(b) Test for a significant relationship by using the t-test. Use α = 0.05.

State the null and alternative hypotheses.

H0: β1 = 0
Ha: β1 ≠ 0

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

Answer:

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

State your conclusion.

Answer: Do not reject H0. We cannot 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
Ha: β1 ≠ 0    

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

Answer:

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

Answer:

What is your conclusion?

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