Question

In a regression analysis involving 27 observations, the following estimated regression equation was developed.

ŷ = 25.2 + 5.5x₁

For this estimated regression equation SST = 1,600 and SSE = 550.

(a) At α = 0.05, test whether x₁ is significant.

State the null and alternative hypotheses.

H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₀ ≠ 0
H_a: β₀ = 0    H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₁ = 0
H_a: β₁ ≠ 0

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

F =

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

p-value =

Is x₁ significant?

A)Reject H₀. We conclude that x₁ is significant.

B)Do not reject H₀. We conclude that x₁ is not significant.    

C)Reject H₀. We conclude that x₁ is not significant.

D)Do not reject H₀. We conclude that x₁ is significant.

Suppose that variables x₂ and x₃ are added to the model and the following regression equation is obtained.

ŷ = 16.3 + 2.3x₁ + 12.1x₂ − 5.8x₃

For this estimated regression equation SST = 1,600 and SSE = 100.

(b) Use an F test and a 0.05 level of significance to determine whether x₂ and x₃ contribute significantly to the model.

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero.
H_a: β₂ = β₃ = 0H₀: β₁ ≠ 0
H_a: β₁ = 0    H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₂ = β₃ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic.

=

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

p-value =

Is the addition of x₂ and x₃ significant?

A)Reject H₀. We conclude that the addition of variables x₂ and x₃ is not significant.

B)Do not reject H₀. We conclude that the addition of variables x₂ and x₃ is significant.   

C)Do not reject H₀. We conclude that the addition of variables x₂ and x₃ is not significant.

D)Reject H₀. We conclude that the addition of variables x₂ and x₃ is significant.

Answer 1

a)

H0: β1 = 0
Ha: β1 ≠ 0

	SS	DF	MS	F	p value
regression	1050	1	1050	47.73	0.0000
error	550	25	22
total	1600	26

F = 47.73

p value=0.000

A)Reject H0. We conclude that x1 is significant.

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b)

H0: β2 = β3 = 0
Ha: One or more of the parameters is not equal to zero.

	SS	DF	MS	F	p value
regression	1500	3	500	115.00	0.00000
error	100	23	4.347826
total	1600	26

test stat=115

p vaue = 0.000

D)Reject H0. We conclude that the addition of variables x2 and x3 is significant.