Question

In: Statistics and Probability

The following estimated regression equation based on 10 observations was presented. ŷ = 21.1370 + 0.5903x1...

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

H_a: β₁ ≥ β₂

H₀: β₁ > β₂

H_a: β₁ ≤ β₂

H₀: β₁ = β₂ = 0

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

H₀: β₁ ≠ 0 and β₂ ≠ 0

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

H₀: β₁ ≠ 0 and β₂ = 0

H_a: 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

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

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

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

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.

Solutions

Expert Solution

orchestra answered 1 year ago

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