In the case when the errors are homoskedastic and normally distributed,conditional on X,then
A) is distributed N(β, ),where = I(k+1).
B) is distributed N(β, ),where = /n = /n.
C) is distributed N(β, ),where = (
X)-1.
D) = PXY where PX = X(
X)-1 .

Question

In the case when the errors are homoskedastic and normally distributed,conditional on X,then
A) is distributed N(β, ),where = I(k+1). 
B) is distributed N(β, ),where = /n = /n. 
C) is distributed N(β, ),where = ( 
X)-1. 
D) = PXY where PX = X( 
X)-1 .

Quizplus · Accepted Answer

The formula for the standard error of the OLS estimator when errors are homoskedastic and normally distributed, conditional on X, is given by (X'X)-1 X'ΩX(X'X)-1, where Ω is the diagonal matrix of error variances. Option C provides the correct expression for Ω, which is the diagonal matrix of residuals squared. Therefore, C is the best choice. Options A and B are incorrect because they provide incorrect expressions for Ω. Option D is incorrect because it does not provide the correct formula for the standard error of the OLS estimator.

In the Case When the Errors Are Homoskedastic and Normally