$E \left( \frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } \right)$
A) is the expected value of the homoskedasticity only standard errors.
B) $= \sigma _ { u } ^ { 2 }$
C) exists only asymptotically.
D) $= \sigma _ { u } ^ { 2 } / ( \mathrm { n } - 2 )$

Question

Quizplus · Accepted Answer

The expression is the expected value of the mean squared error of the residuals, which is an unbiased estimator of the variance of the error term $\sigma_u^2$ in a linear regression model.

E(1n−2∑i=1nu^i2)E \left( \frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } \right)E(n−21​∑i=1n​u^i2​)

$E \left( \frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } \right)$