Given a dataset {y, X1, X2}=1,2,... Let the SLR OLS estimators and fitted value be yi...
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Given a dataset {y₁, X₁1, X₁2}=1,2,... Let the SLR OLS estimators and fitted value be yi = Bo + B1X11, and the MLR OLS estimators and fitted value be ŷ₁ = Bo + B₁x₁1 + B₂x₁2. (20 marks) (a) Show that SSR, SSRur= (₂) Eif, where SSR, and SSRur are the SSR for the SLR and MLR, respectively, and fiz is the OLS residual from the regression of x2 on X₁₁ with an intercept. (20 marks) (b) For the test Ho: B2 = 0 vs. H₁: B₂ # 0, show that the F-statistic is the square of the t-statistic. Argue that the t-test and the F-test are equivalent for a single-restriction hypothesis. Given a dataset {y₁, X₁1, X₁2}=1,2,... Let the SLR OLS estimators and fitted value be yi = Bo + B1X11, and the MLR OLS estimators and fitted value be ŷ₁ = Bo + B₁x₁1 + B₂x₁2. (20 marks) (a) Show that SSR, SSRur= (₂) Eif, where SSR, and SSRur are the SSR for the SLR and MLR, respectively, and fiz is the OLS residual from the regression of x2 on X₁₁ with an intercept. (20 marks) (b) For the test Ho: B2 = 0 vs. H₁: B₂ # 0, show that the F-statistic is the square of the t-statistic. Argue that the t-test and the F-test are equivalent for a single-restriction hypothesis.
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Related Book For
Mathematical Statistics with Applications in R
ISBN: 978-0124171138
2nd edition
Authors: Chris P. Tsokos, K.M. Ramachandran
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