Question

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

ŷ = 21.1370 + 0.5509x₁ + 0.4980x₂

Here, SST = 6,724.125, SSR = 6,222.375, s_b1 = 0.0814, and s_b2 = 0.0565.

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

MSR=

MSE=

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

2a. State the null and alternative hypotheses.

(a) H₀: β₁ = β₂ = 0

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

(b) H₀: β₁ ≠ 0 and β₂ ≠ 0

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

    

(c) H₀: β₁ < β₂

H_a: β₁ ≥ β₂

(d)H₀: β₁ > β₂

H_a: β₁ ≤ β₂

(e) H₀: β₁ ≠ 0 and β₂ = 0

H_a: β₁ = 0 and β₂ ≠ 0

2b. Find the value of the test statistic. (Round your answer to two decimal places.)

F =

2c. Find the p-value. (Round your answer to three decimal places.)

p-value =

2d. State your conclusion.

(a) Reject H₀. There is sufficient evidence to conclude that the overall model is significant.

(b) Do not reject H₀. There is sufficient evidence to conclude that the overall model is significant.    

(c) Reject H₀. There is insufficient evidence to conclude that the overall model is significant.

(d) Do not reject H₀. There is insufficient evidence to conclude that the overall model is significant.

3. Perform a t test for the significance of β₁. Use α = 0.05.

3a. State the null and alternative hypotheses.

(a) H₀: β₁ ≠ 0

H_a: β₁ = 0

(b)H₀: β₁ < 0

H_a: β₁ ≥ 0

    

(c)H₀: β₁ = 0

H_a: β₁ > 0

(d)H₀: β₁ = 0

H_a: β₁ ≠ 0

(e) H₀: β₁ > 0

H_a: β₁ ≤ 0

3b. Find the value of the test statistic. (Round your answer to two decimal places.)

t =

3c. Find the p-value. (Round your answer to three decimal places.)

p-value =

3d. State your conclusion.

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

(b) Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.   

(c) Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(d) Reject H₀. There is insufficient evidence to conclude that β₁ is significant.

4. Perform a t test for the significance of β₂. Use α = 0.05.

4a. State the null and alternative hypotheses.

(a)H₀: β₂ ≠ 0

H_a: β₂ = 0

(b) H₀: β₂ < 0

H_a: β₂ ≥ 0

    

(c) H₀: β₂ = 0

H_a: β₂ ≠ 0

(d) H₀: β₂ = 0

H_a: β₂ > 0

(e) H₀: β₂ > 0

H_a: β₂ ≤ 0

4b. Find the value of the test statistic. (Round your answer to two decimal places.)

t =

4c. Find the p-value. (Round your answer to three decimal places.)

p-value =

4d. State your conclusion.

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

(b) Reject H₀. There is insufficient evidence to conclude that β₂ is significant.    

(c) Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.

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

Answer 1

1)

p=number of independent variables=				2
MSR =SSR/p =		3111.188
MSE=(SSE/(n-p-1))=		71.679

2)

2a)

(a) H₀: β₁ = β₂ = 0

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

2b)

2b. Find the value of the test statistic =43.40

p value =0.000

2d) (a) Reject H₀. There is sufficient evidence to conclude that the overall model is significant.

3a)option d

b)

t test statistic =coefficient/standard error =

6.77

c)

p value =

0.000

d) (a) Reject H₀. There is sufficient evidence to conclude that β₁ is significant.

4a)option C

b)

t test statistic =coefficient/standard error =

8.81

c) p vaklue =0.000

d) (a) Reject H₀. There is sufficient evidence to conclude that β₂ is significant.