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5. Consider the simple linear regression model given by Yi=1+2Xi+ui (.pdf

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5. Consider the simple linear regression model given by Yi=1+2Xi+ui (a) Show that Coo(Y,p^2^)=0. (b) Show that Cow(1,2)=XVar(^2) (c) Show that Cor(Y,Y)=Cor(Y,X) 6. Suppoie the intercept of simple linear regresion model is known as 5. One can consider the model Yi=5+Xi+i for i=1,,n,E(ui)=0,Var(ui)=1. Find the OLS etinator. ^, E(),Var(^). 7. Consider the simple linear regression given by Yi=1+2Xi+wi But instead of assunaing E(ux)=0, suppose otie assume E(ux)=3 Obtain OLS estimator ^1,2,.

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5. Consider the simple linear regression model given by Yi=1+2Xi+ui (a) Show that Coo(Y,p^2^)=0. (b) Show that Cow(1,2)=XVar(^2) (c) Show that Cor(Y,Y)=Cor(Y,X) 6. Suppoie the intercept of simple linear regresion model is known as 5. One can consider the model Yi=5+Xi+i for i=1,,n,E(ui)=0,Var(ui)=1. Find the OLS etinator. ^, E(),Var(^). 7. Consider the simple linear regression given by Yi=1+2Xi+wi But instead of assunaing E(ux)=0, suppose otie assume E(ux)=3 Obtain OLS estimator ^1,2,

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