3. Consider a linear regression model: yi x' = (Xi1, ..., Xik) and B = (B,...,...

 

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3. Consider a linear regression model: yi x' = (Xi1, ..., Xik) and B = (B,..., k)'. (i) Show that E(xu) = 0 (show how you obtain the result, explain your proof). (ii) Replacing ui by ui = yi - x' in E(xiui) = 0, we obtain E[xi(yi x;)] = 0. x'; + ui, i = 1,..., n, with E(u|x;) = 0, where Solve for from this equation. (iii) Replacing expectation (population mean) by sample mean in (ii) gives estimator for B. This is called a method of moment estimator (since it is derived from a moment condition E(xU) 0). What is the relationship between this method of moment estimator and the least squares estimator we derived in class? = 3. Consider a linear regression model: yi x' = (Xi1, ..., Xik) and B = (B,..., k)'. (i) Show that E(xu) = 0 (show how you obtain the result, explain your proof). (ii) Replacing ui by ui = yi - x' in E(xiui) = 0, we obtain E[xi(yi x;)] = 0. x'; + ui, i = 1,..., n, with E(u|x;) = 0, where Solve for from this equation. (iii) Replacing expectation (population mean) by sample mean in (ii) gives estimator for B. This is called a method of moment estimator (since it is derived from a moment condition E(xU) 0). What is the relationship between this method of moment estimator and the least squares estimator we derived in class? =

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i To show Exiui 0 By the property of conditional expectation Euixi 0 Takin... View the full answer