Question

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^=σ2SSTj1−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.

Answer 1

1. Variance of beta decreases as SST increases.

2. option a

Explanation:

SST is same as total sum of squares. From the formula above, if the value of SST increases, the variance of beta decreases.

In this model, if the sample size n is increased, the the sampling variance beta is going to reduce. The variance of the distribution is population variance / the size of the sample n. so the bigger n becomes, the lower the sampling variance of beta.