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)= $\sigma _ { u } ^ { 2 }$ /(n-2).

Question

Quizplus · Accepted Answer

The expression represents the expected value of the squared residuals ($\hat { u } _ { i } ^ { 2 }$) from a regression model, averaged over the sample size minus 2. This is an unbiased estimator of the variance of the error term ($\sigma _ { u } ^ { 2 }$) in the population, assuming the model is correctly specified and the errors are homoskedastic and independently distributed.

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

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