The following estimated regression equation based on 10 observations was presented ŷ = 25.1270 + 0.5309x1 + 0.4920x2 Here, SST = 6,738.125, SSR = 6,221.375, sb1 = 0.0818, and sb2 = 0.0563. Compute MSR and MSE. (Round your answers to three decimal places.) Compute F and perform the appropriate F test. Use α = 0.05. State the null and alternative hypotheses. a. H0: β1 ≠ 0 and β2 ≠ 0 Ha: One or more of the parameters is equal to zero. b. H0: β1 = β2 = 0 Ha: One or more of the parameters is not equal to zero. c. H0: β1 > β2 Ha: β1 ≤ β2 H0: β1 < β2 Ha: β1 ≥ β2d. H0: β1 ≠ 0 and β2 = 0 Ha: β1 = 0 and β2 ≠ 0 2. Find the value of the test statistic. (Round your answer to two decimal places.) 3. Find the p-value. (Round your answer to three decimal places.) p-value = 4. 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.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 40RE: For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina...

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The following estimated regression equation based on 10 observations was presented

ŷ = 25.1270 + 0.5309x₁ + 0.4920x₂

Here, SST = 6,738.125, SSR = 6,221.375,

s_b1 = 0.0818,

and

s_b2 = 0.0563.

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

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

State the null and alternative hypotheses.

H₀: β₁ ≠ 0 and β₂ ≠ 0

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

H₀: β₁ = β₂ = 0

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

H₀: β₁ > β₂

H_a: β₁ ≤ β₂

H₀: β₁ < β₂

H_a: β₁ ≥ β₂

H₀: β₁ ≠ 0 and β₂ = 0

H_a: β₁ = 0 and β₂ ≠ 0

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

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

p-value =

4. 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.

4. Perform a t test for the significance of

β₁.

Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ > 0

H_a: β₁ ≤ 0

H₀: β₁ ≠ 0

H_a: β₁ = 0

H₀: β₁ < 0

H_a: β₁ ≥ 0

H₀: β₁ = 0

H_a: β₁ > 0

H₀: β₁ = 0

H_a: β₁ ≠ 0

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

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

p-value =

7. State your conclusion.

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

b. Reject H₀. There is insufficient evidence to conclude that β₁ is significant.

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

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

8. Perform a t test for the significance of

β₂.

Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₂ ≠ 0

H_a: β₂ = 0

H₀: β₂ = 0

H_a: β₂ ≠ 0

H₀: β₂ > 0

H_a: β₂ ≤ 0

H₀: β₂ < 0

H_a: β₂ ≥ 0

H₀: β₂ = 0

H_a: β₂ > 0

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

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

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