The components of the OLS variances Under assumptions MLR.1 through MLR.5, conditional on the sample values of the independent variables, the variance of βjˆβj^ under OLS is: Var(βjˆ)=σ2SSTj(1−R2j)Var⁡βj^=σ2SST j1−Rj2
where
σ2 = the variance of the error term
SSTj = the total sample variation of xj
Rj2 = the R-squared from a regression of xj on all of the other explanatory variables, along with an intercept parameter.
The variance of β as SST, increases
For the given model, which of the following would lead to a reduction of the sampling variance of β?
a. Increasing the sample size.
b. Adding irrelevant explanatory variables to the model that are correlated with X.
c. Adding an explanatory variable that is equal to 1-x.
d. Decreasing the sample size.