In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

= 17.6 + 3.8x₁ 2.3x₂ + 7.6x₃ + 2.7x₄

For this estimated regression equation, SST = 1,805 and SSR = 1,760.

(a)At = 0.05, test the significance of the relationship among the variables.

State the null and alternative hypotheses.H₀: ₁ = ₂ = ₃ = ₄ = 0

H_a: One or more of the parameters is not equal to zero.

H₀: ₀ = ₁ = ₂ = ₃ = ₄ = 0 H_a: One or more of the parameters is not equal to zero.

H₀: One or more of the parameters is not equal to zero. H_a: ₁ = ₂ = ₃ = ₄ = 0H₀:

One or more of the parameters is not equal to zero. H_a: ₀ = ₁ = ₂ = ₃ = ₄ = 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 =

State your conclusion

Do not reject H₀. We conclude that the overall relationship is not significant.

Do not reject H₀. We conclude that the overall relationship is significant.

Reject H₀. We conclude that the overall relationship is not significant.

Reject H₀. We conclude that the overall relationship is significant.

Suppose variables x₁ and x₄ are dropped from the model and the following estimated regression equation is obtained.

= 11.1 3.6x₂ + 8.1x₃

For this model, SST = 1,805 and SSR = 1,705.

(b)Compute SSE(x₁, x₂, x₃, x₄).

SSE(x₁, x₂, x₃, x₄)=

(c)Compute SSE(x₂, x₃).

SSE(x₂, x₃) =

(d)Use an F test and a 0.05 level of significance to determine whether x₁ and x₄ 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: ₁ = ₄ = 0H₀:

One or more of the parameters is not equal to zero. H_a: ₂ = ₃ = 0

H₀: ₂ = ₃ = 0 H_a: One or more of the parameters is not equal to zero.

H₀: ₁ = ₄ = 0 H_a: One or more of the parameters is not equal to zero.

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.

Do not reject H₀. We conclude that x₁ and x₄ do not contribute significantly to the model.

Do not reject H₀. We conclude that x₁ and x₄ contribute significantly to the model.

Reject H₀. We conclude that x₁ and x₄ contribute significantly to the model.

Reject H₀. We conclude that x₁ and x₄ do not contribute significantly to the model.