3) The following estimated regression equation based on 10 observations was presented. ŷ = 29.1470 + 0.5901x1 + 0.4960x2

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3) The following estimated regression equation based on 10observations was presented.
ŷ = 29.1470 + 0.5901x1 + 0.4960x2
Here, SST = 6,732.125, SSR = 6,228.375,
sb1 = 0.0812,
and
sb2 = 0.0563.
(a)
Compute MSR and MSE. (Round your answers to three decimalplaces.)
MSR=MSE=
(b)
Compute F and perform theappropriate F test. Use 𝛼 = 0.05.
State the null and alternative hypotheses.
Find the value of the test statistic. (Round your answer to twodecimal places.)
F =
Find the p-value. (Round your answer to threedecimal places.)
p-value =
State your conclusion.
Reject H0. There is sufficient evidenceto conclude that the overall model is significant.Do notreject H0. There is sufficient evidence toconclude that the overall model issignificant. Reject H0.There is insufficient evidence to conclude that the overall modelis significant.Do not reject H0. There isinsufficient evidence to conclude that the overall model issignificant.
(c)
Perform a t test for the significanceof
𝛽1.
Use 𝛼 = 0.05.
State the null and alternative hypotheses.
Find the value of the test statistic. (Round your answer to twodecimal places.)
t =
Find the p-value. (Round your answer to threedecimal places.)
p-value =
State your conclusion.
Reject H0. There is insufficientevidence to conclude that 𝛽1 is significant.Donot reject H0. There is insufficientevidence to conclude that 𝛽1 issignificant. Do notreject H0. There is sufficient evidence toconclude that 𝛽1 issignificant.Reject H0. There is sufficientevidence to conclude that 𝛽1 issignificant.
(d)
Perform a t test for the significanceof
𝛽2.
Use 𝛼 = 0.05.
State the null and alternative hypotheses.
Find the value of the test statistic. (Round your answer to twodecimal places.)
t =
Find the p-value. (Round your answer to threedecimal places.)
p-value =
State your conclusion.
Reject H0. There is sufficient evidenceto conclude that 𝛽2 issignificant.Reject H0. There isinsufficient evidence to conclude that 𝛽2 issignificant. Do notreject H0. There is sufficient evidence toconclude that 𝛽2 is significant.Do notreject H0. There is insufficient evidenceto conclude that 𝛽2 is significant.

3 The Following Estimated Regression Equation Based On 10 Observations Was Presented Y 29 1470 0 5901x1 0 4960x2 1 (160.81 KiB) Viewed 10 times

3 The Following Estimated Regression Equation Based On 10 Observations Was Presented Y 29 1470 0 5901x1 0 4960x2 2 (98.77 KiB) Viewed 10 times

The following estimated regression equation based on 10 observations was presented. ŷ = 29.1470 +0.5901x₁ + 0.4960x2 Here, SST = 6,732.125, SSR = 6,228.375, Sb1 (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR = MSE = = 0.0812, and >b2 (b) Compute F and perform the appropriate F test. Use α = 0.05. State the null and alternative hypotheses. Ho: P₁0 and ₂ = 0 H₂: B₁: = 0 and B₂ # 0 Ho: B₁ < B₂ Ha: B₁ ZB₂ Ho: P1 = P₂ = 0 H₂: One or more of the parameters is not equal to zero. Ho: B₁ > B₂ H₂: B₁ = B₂ = 0.0563. Ho: B₁0 and ₂ #0 H₂: One or more of the parameters is equal to zero. 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. O Reject Ho. There is sufficient evidence to conclude that the overall model is significant. Do not reject Ho. There is sufficient evidence to conclude that the overall model is significant. O Reject Ho. There is insufficient evidence to conclude that the overall model is significant. O Do not reject Ho. There is insufficient evidence to conclude that the overall model is significant.
(c) Perform a t test for the significance of ß₁. Use α = 0.05. State the null and alternative hypotheses. Ho: B₁ = = 0 Ha: B₁ > 0 Ho: B₁ * 0 Ha: P₁ = = 0 Ho: B₁ = 0 Ha: B₁ * 0 Ho: B₁ > 0 Ha: B₁ ≤ 0 Ho: B₁< Ha: B₁ ≥ 0 <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. O Reject Ho. There is insufficient evidence to conclude that B₂₁ is significant. O Do not reject Ho. There is insufficient evidence to conclude that ₁ is significant. O Do not reject Ho. There is sufficient evidence to conclude that ₁ is significant. O Reject Ho. There is sufficient evidence to conclude that B₁ is significant. (d) Perform a t test for the significance of ß₂. Use α = 0.05. State the null and alternative hypotheses. Ho: B₂ #0 H₂: P₂= = 0 Ho: B₂ = 0 Ha: B₂ > 0 Ho: B₂ > 0 Ha: B₂ ≤0 = 0 Ho: B₂= Ha: B₂ #0 Ho: B₂< Ha: B₂ ≥ 0 <0 Find the value of the test statistic. (Round your answer to two decimal places.) t =