Multiple Choice Question What is the formula for the test statistic used to test individual coefficients of the multiple regression equation? O F = $\frac{si^2}{sb^2}$ O t = $\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$ O t = $\frac{bi-0}{sbi}$
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Hi Guys Please assist with the following
Ivan K.
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 = 1805 and SSR = 1760. a. At α = .05, test the significance of the relationship among the variables. If your answer is zero, enter "0". Use Table 4 in Appendix B. F = 244.44 (to 2 decimals) p-value = We conclude that the model 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 = 1805 and SSR = 1705. b. Compute SSE(x₁, x₂, x₃, x₄). 45 c. Compute SSE(x₂, x₃). 100 d. Use an F test and a .05 level of significance to determine whether x₁ and x₄ contribute significantly to the model. If your answer is zero, enter "0". Use Table 4 in Appendix B. F = 15.28 (to 2 decimals) p-value = Variables x₁ and x₄ do contribute to the model.
Sarah G.
Consider the simple regression model yi = Bo + B1xi + ̄i. The Gauss-Markov conditions hold and in addition ̄i ~ N(0, ̃). a. Show that when we test H0 : B1 = 0 against Ha : B1 ≠ 0 we can express F = (R^2 / (1 - R^2))(n - 2), where R^2 = SSR / SST. b. Suppose we are testing the hypothesis H0 : B1 = 0 against Ha : B1 ≠ 0. The F statistics can be expressed as F = (ẞ1^2 ∑(xi - x̄)^2) / se^2. Find the expected value of F under H0. Note: ẞ1, se^2 are independent. Also, if Q ~ Γ(α, β) then EQ^k = (Γ(α + k)β^k) / Γ(α).
Adi S.
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