Question

You may need to use the appropriate technology to answer this 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 = 1,550 and SSE = 550.

(a)

At α = 0.05, test whether

x₁

is significant.

State the null and alternative hypotheses.

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

Do not reject H₀. We conclude that x₁ is not significant.Reject H₀. We conclude that x₁ is significant.    Reject H₀. We conclude that x₁ is not significant.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 = 1,550 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: β₂ = β₃ = 0
H_a: One or more of the parameters is not equal to zero.    H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₁ = 0
H_a: β₁ ≠ 0

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?

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

Answer 1