You may need to use the appropriate technology to answer this question. In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation, SST = 1,825 and SSR = 1,780. (a) At ? = 0.05, test the significance of the relationship among the variables. State the null and alternative hypotheses. H0: One or more of the parameters is not equal to zero. Ha: ?1 = ?2 = ?3 = ?4 = 0H0: One or more of the parameters is not equal to zero. Ha: ?0 = ?1 = ?2 = ?3 = ?4 = 0 H0: ?0 = ?1 = ?2 = ?3 = ?4 = 0 Ha: One or more of the parameters is not equal to zero.H0: ?1 = ?2 = ?3 = ?4 = 0 Ha: One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the overall relationship is not significant.Reject H0. We conclude that the overall relationship is not significant. Reject H0. We conclude that the overall relationship is significant.Do not reject H0. We conclude that the overall relationship is significant. Suppose variables x1 and x4 are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1 − 3.6x2 + 8.1x3 For this model, SST = 1,825 and SSR = 1,725. (b) Compute SSE(x1, x2, x3, x4). SSE(x1, x2, x3, x4) = (c) Compute SSE(x2, x3). SSE(x2, x3) = (d) Use an F test and a 0.05 level of significance to determine whether x1 and x4 contribute significantly to the model. State the null and alternative hypotheses. H0: One or more of the parameters is not equal to zero. Ha: ?1 = ?4 = 0H0: One or more of the parameters is not equal to zero. Ha: ?2 = ?3 = 0 H0: ?2 = ?3 = 0 Ha: One or more of the parameters is not equal to zero.H0: ?1 = ?4 = 0 Ha: One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value =

You may need to use the appropriate technology to answer this question. In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation, SST = 1,825 and SSR = 1,780. (a) At ? = 0.05, test the significance of the relationship among the variables. State the null and alternative hypotheses. H0: One or more of the parameters is not equal to zero. Ha: ?1 = ?2 = ?3 = ?4 = 0H0: One or more of the parameters is not equal to zero. Ha: ?0 = ?1 = ?2 = ?3 = ?4 = 0 H0: ?0 = ?1 = ?2 = ?3 = ?4 = 0 Ha: One or more of the parameters is not equal to zero.H0: ?1 = ?2 = ?3 = ?4 = 0 Ha: One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the overall relationship is not significant.Reject H0. We conclude that the overall relationship is not significant. Reject H0. We conclude that the overall relationship is significant.Do not reject H0. We conclude that the overall relationship is significant. Suppose variables x1 and x4 are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1 − 3.6x2 + 8.1x3 For this model, SST = 1,825 and SSR = 1,725. (b) Compute SSE(x1, x2, x3, x4). SSE(x1, x2, x3, x4) = (c) Compute SSE(x2, x3). SSE(x2, x3) = (d) Use an F test and a 0.05 level of significance to determine whether x1 and x4 contribute significantly to the model. State the null and alternative hypotheses. H0: One or more of the parameters is not equal to zero. Ha: ?1 = ?4 = 0H0: One or more of the parameters is not equal to zero. Ha: ?2 = ?3 = 0 H0: ?2 = ?3 = 0 Ha: One or more of the parameters is not equal to zero.H0: ?1 = ?4 = 0 Ha: One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You may need to use the appropriate technology to answer this question.

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

ŷ = 17.6 + 3.8x₁ − 2.3x₂ + 7.6x₃ + 2.7x₄

For this estimated regression equation, SST = 1,825 and SSR = 1,780.

(a)

At ? = 0.05, test the significance of the relationship among the variables.

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero.
H_a: ?₁ = ?₂ = ?₃ = ?₄ = 0H₀: One or more of the parameters is not equal to zero.
H_a: ?₀ = ?₁ = ?₂ = ?₃ = ?₄ = 0 H₀: ?₀ = ?₁ = ?₂ = ?₃ = ?₄ = 0
H_a: One or more of the parameters is not equal to zero.H₀: ?₁ = ?₂ = ?₃ = ?₄ = 0
H_a: One or more of the parameters is not equal to zero.

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

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

p-value =

State your conclusion.

Do not reject H₀. We conclude that the overall relationship is not significant.Reject H₀. We conclude that the overall relationship is not significant. Reject H₀. We conclude that the overall relationship is significant.Do not reject H₀. We conclude that the overall relationship is significant.

Suppose variables

x₁ and x₄

are dropped from the model and the following estimated regression equation is obtained.

ŷ = 11.1 − 3.6x₂ + 8.1x₃

For this model, SST = 1,825 and SSR = 1,725.

(b)

Compute

SSE(x₁, x₂, x₃, x₄).

SSE(x₁, x₂, x₃, x₄)

(c)

Compute

SSE(x₂, x₃).

SSE(x₂, x₃)

(d)

Use an F test and a 0.05 level of significance to determine whether

x₁ and x₄

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: ?₁ = ?₄ = 0H₀: One or more of the parameters is not equal to zero.
H_a: ?₂ = ?₃ = 0 H₀: ?₂ = ?₃ = 0
H_a: One or more of the parameters is not equal to zero.H₀: ?₁ = ?₄ = 0
H_a: One or more of the parameters is not equal to zero.

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

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

p-value =

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