The variance of the OLS estimatorchoose the right option(s):O a.increases as the number of observations increaseso b.increases as the variance of the unobservable increasesoc.decreases as the number of observations increases d.decreases as the variance of the unobservable increases
Question
The variance of the OLS estimatorchoose the right option(s):O a.increases as the number of observations increaseso b.increases as the variance of the unobservable increasesoc.decreases as the number of observations increases d.decreases as the variance of the unobservable increases
Solution
The correct options are:
b. Increases as the variance of the unobservable increases c. Decreases as the number of observations increases
Explanation:
Option b is correct because the variance of the OLS (Ordinary Least Squares) estimator is directly proportional to the variance of the error term. If the variance of the unobservable (error term) increases, the variance of the OLS estimator also increases.
Option c is correct because the variance of the OLS estimator is inversely proportional to the number of observations. As the number of observations increases, the variance of the OLS estimator decreases. This is because with more data, the estimator can make more accurate predictions, reducing its variance.
Option a is incorrect because the variance of the OLS estimator decreases, not increases, as the number of observations increases.
Option d is incorrect because the variance of the OLS estimator increases, not decreases, as the variance of the unobservable increases.
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