Question

The following estimated regression equation based on 10 observations was presented.

ŷ = 21.1370 + 0.5903x₁ + 0.4920x₂

Here, SST = 6,736.125, SSR = 6,228.375,

s_b1 = 0.0819,

and

s_b2 = 0.0563.

(a)

Compute MSR and MSE. (Round your answers to three decimal places.)

MSR=MSE=

(b)

Compute F and perform the appropriate F test. Use α = 0.05.

State the null and alternative hypotheses.

H0: β1 < β2

Ha: β1 ≥ β2

H0: β1 > β2

Ha: β1 ≤ β2

    

H0: β1 = β2 = 0

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

H0: β1 ≠ 0 and β2 ≠ 0

Ha: One or more of the parameters is equal to zero.

H0: β1 ≠ 0 and β2 = 0

Ha: β1 = 0 and β2 ≠ 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 =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that the overall model is significant.Do not reject H₀. There is sufficient evidence to conclude that the overall model is significant.    Reject H₀. There is insufficient evidence to conclude that the overall model is significant.Do not reject H₀. There is insufficient evidence to conclude that the overall model is significant.

(c)

Perform a t test for the significance of

β₁.

Use α = 0.05.

State the null and alternative hypotheses.

H0: β1 < 0

Ha: β1 ≥ 0

H0: β1 ≠ 0

Ha: β1 = 0

    

H0: β1 = 0

Ha: β1 ≠ 0

H0: β1 = 0

Ha: β1 > 0

H0: β1 > 0

Ha: β1 ≤ 0

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

t =

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

p-value =

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.Reject H₀. There is sufficient evidence to conclude that β₁ is significant.    Reject H₀. There is insufficient evidence to conclude that β₁ is significant.Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(d)

Perform a t test for the significance of

β₂.

Use α = 0.05.

State the null and alternative hypotheses.

H0: β2 = 0

Ha: β2 ≠ 0

H0: β2 < 0

Ha: β2 ≥ 0

    

H0: β2 > 0

Ha: β2 ≤ 0

H0: β2 = 0

Ha: β2 > 0

H0: β2 ≠ 0

Ha: β2 = 0

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

t =

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

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.Reject H₀.

There is insufficient evidence to conclude that β₂ is significant.   

Do not reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Reject H₀. There is sufficient evidence to conclude that β₂ is significant.

Answer 1