Question

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

ŷ = 27.1570 + 0.5107x₁ + 0.4940x₂

Here, SST = 6,722.125, SSR = 6,223.375,

s_b1 = 0.0811,

and

s_b2 = 0.0569.

(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 = 0

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

    

H0: β1 ≠ 0 and β2 = 0

Ha: β1 = 0 and β2 ≠ 0

H0: β1 ≠ 0 and β2 ≠ 0

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

H0: β1 < β2

Ha: β1 ≥ β2

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.

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.    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.

(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.

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

Answer 1

Since number of observations is 10 and number of independent variables is 2 so

(a)

(b)

H0: β1 = β2 = 0

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

The F test statistics is

The p-value using excel function "=FDIST(43.67,2,7)" is 0.0001

Since p-value is less than 0.05 so we reject the null hypothesis.

Correct option: .Reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(c)

H0: β1 = 0

Ha: β1 ≠ 0

The test statistics is

Degree of freedom: df=7

The p-value using excel function "=TDIST(6.3,7,2)" is 0.0004

Reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(d)

H0: β2 = 0

Ha: β2 ≠ 0

The test statistics is

Degree of freedom: df=7

The p-value using excel function "=TDIST(8.68,7,2)" is 0.0001

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