In (4-13), we find that when superfluous variables X 2 are added to the regression of y

Question:

In (4-13), we find that when superfluous variables X² are added to the regression of y on X₁ the least squares coefficient estimator is an unbiased estimator of the true parameter vector, β = (β'₁, 0')'. Show that in this long regression, e'e/(n−K₁−K₂) is also unbiased as estimator of σ².