12. 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 B, under OLS is: Var () where o - the variance of the error term SST, - the total sample variation of z, RỆ - the R-squared from a regression of z, on all of the other explanatory variables, along with an intercept parameter The variance of By ▼ as R increases. decreases For the given mode e following would lead to a reduction of the sampling variance of 37 increases O Adding al variable that is equal to 5 + z, O using the same data set with the same number of observations O Adding irrelevant explanatory variables to the model that are correlated with zy O Choosing an explanatory variable za that is uncorrelated with the other explanatory variables in the model

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12. 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 B; under OLS is:
Var (B)
sST, (1-15)
where
o2 = the variance of the error term
SST; = the total sample variation of a;
R; = the R-squared from a regression of r; on all of the other explanatory variables, along with an intercept parameter
The variance of Bi
v as R; increases.
decreases
For the given mode
e following would lead to a reduction of the sampling variance of B;?
increases
O Adding
variable that is equal to 5+ *j
O Using the same data set with the same number of observations
O Adding irrelevant explanatory variables to the model that are correlated with r;
O Choosing an explanatory variable z that is uncorrelated with the other explanatory variables in the model
Transcribed Image Text:12. 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 B; under OLS is: Var (B) sST, (1-15) where o2 = the variance of the error term SST; = the total sample variation of a; R; = the R-squared from a regression of r; on all of the other explanatory variables, along with an intercept parameter The variance of Bi v as R; increases. decreases For the given mode e following would lead to a reduction of the sampling variance of B;? increases O Adding variable that is equal to 5+ *j O Using the same data set with the same number of observations O Adding irrelevant explanatory variables to the model that are correlated with r; O Choosing an explanatory variable z that is uncorrelated with the other explanatory variables in the model
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