Question

Or the following PRF estimated using OLS: Yi =β₁ +β₂ Xᵢ +uᵢ if everything else is the same,

β₂ estimates β₂ more precisely when Var(ui ∣Xi ) is larger.
A. True
B.False?

Answer 1

False. When the variance of the error term Var(ui | Xi) is larger, the estimation of the slope coefficient β₂ becomes more precise.

Step-by-step explanation:

False.

When the variance of the error term Var(ui | Xi) is larger, it indicates that the data points are more spread out around the regression line. In this case, the estimation of the slope coefficient β₂ becomes more precise because the larger variability in the error term allows for a better fit of the regression line to the data points. Therefore, we can conclude that the statement is false.