Consider the linear regression model, with ~ N(0, 2) and Elec;]=0 for i #j. N Y...

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Consider the linear regression model, with ~ N(0, 2) and Elec;]=0 for i #j. N Y₁ = Bo + 3₁X₁ + E (a) Show that (X₁) = 0. Please solve the problems without using matrix or vector notation. (b) Prove that the least squares estimators 30 and 3₁ are uncorrelated if and only if 1 X₁ = 0. (c) In the case where E1 X=0, write out an expression for the least squares estimators of 30 and 31. Consider the linear regression model, with ~ N(0, 2) and Elec;]=0 for i #j. N Y₁ = Bo + 3₁X₁ + E (a) Show that (X₁) = 0. Please solve the problems without using matrix or vector notation. (b) Prove that the least squares estimators 30 and 3₁ are uncorrelated if and only if 1 X₁ = 0. (c) In the case where E1 X=0, write out an expression for the least squares estimators of 30 and 31.

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a by Y bz where bi Now by Hence bo Yb aiYi where ai i1 since Y 1x x Y ... View the full answer