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Given that we have a linear model y =XB+e where y denotes an n x1 vector of dependent variable observations, X is an nx k design matrix with a column of 1's in the first column, followed by k-1 columns of k-1 independent variables with n observations per variable and e is an nx1 vector of error terms. Given the following assumptions, E(e) =0, Cov(e)-o, , and the independent variables are fixed (non- stochastic). For the estimator Bos =(X'T'X)" x'Y'y. which of the following statements about the %3D expectation of the estimator is false? ect one: E(Bas)-(X'T'x) E(B)X'r 'X b. None of the other responses are false. E(Pas)- E(x'Y'x)" x'y (Xp + ) C. GLS E(bo)- d. OLS E(Ba)-(XT'x)"x'T 'XE(P) e. POLS E(Ba) - E(B+(X'Y'x)"x'r'e) GLS

Given that we have a linear model y =XB+e where y denotes an n x1 vector of dependent variable observations, X is an nx k design matrix with a column of 1's in the first column, followed by k-1 columns of k-1 independent variables with n observations per variable and e is an nx1 vector of error terms. Given the following assumptions, E(e) =0, Cov(e)-o, , and the independent variables are fixed (non- stochastic). For the estimator Bos =(X'T'X)" x'Y'y. which of the following statements about the %3D expectation of the estimator is false? ect one: E(Bas)-(X'T'x) E(B)X'r 'X b. None of the other responses are false. E(Pas)- E(x'Y'x)" x'y (Xp + ) C. GLS E(bo)- d. OLS E(Ba)-(XT'x)"x'T 'XE(P) e. POLS E(Ba) - E(B+(X'Y'x)"x'r'e) GLS

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 50EQ
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Given that we have a linear model y = Xß + e where y denotes an nx1 vector of dependent variable %3! observations, X is an n x k design matrix with a column of l's in the first column, followed by k-1 columns of k-1 independent variables with n observations per variable and E is an nx1 vector of error terms. Given the following assumptions, E(e) = 0, Cov(t)-oY, , and the independent variables are fixed (non- stochastic). For the estimator ßos =(X'T'X)"x'T'y, which of the following statements about the expectation of the estimator is false? Select one: Oa. E(Ba)-(X'T'x) E(B)X'T'x GLS O b. None of the other responses are false. OF E(Bos) = E(X'T'x)*x'r*(XP +e}) •d. E(Bos) =. POLS Oe. E(Bas)=(X'y'x)"x'T 'XE(B) GLS E(Bas)=E(B+(XY'x)"x'T'e) GLS
Transcribed Image Text:Given that we have a linear model y = Xß + e where y denotes an nx1 vector of dependent variable %3! observations, X is an n x k design matrix with a column of l's in the first column, followed by k-1 columns of k-1 independent variables with n observations per variable and E is an nx1 vector of error terms. Given the following assumptions, E(e) = 0, Cov(t)-oY, , and the independent variables are fixed (non- stochastic). For the estimator ßos =(X'T'X)"x'T'y, which of the following statements about the expectation of the estimator is false? Select one: Oa. E(Ba)-(X'T'x) E(B)X'T'x GLS O b. None of the other responses are false. OF E(Bos) = E(X'T'x)*x'r*(XP +e}) •d. E(Bos) =. POLS Oe. E(Bas)=(X'y'x)"x'T 'XE(B) GLS E(Bas)=E(B+(XY'x)"x'T'e) GLS
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