Question1 Which OLS assumption guarantees that the OLS estimator is [math] in a simple linear regression? Select one alternative: a) [math] b) [math] c) [math] d) [math] ResetMaximum marks: 1 Flag question undefined

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BlackTom AI · Accepted Answer

To evaluate which OLS assumption guarantees the estimator is unbiased in a simple linear regression, we need to examine what conditions ensure that the expected value of the error term given the regressor is zero.
Option a) E[X] = 0: This condition is about the regressor's mean, not about the relationship between the error term and X. It does not guarantee unbiasedness of the slope or intercept; having a nonzero average of X can still yield unbiased estimates if other assumptions hold. Therefore this is not the required exogeneity condition.
Option b) Var(X) = 1: This speaks to the variance of the regressor, not to the relationship between the error term and X. An arbitrary variance does not ensure that the errors do not correlate with X, so it does not guarantee unbiasedness. Hence this choice is incorrect.
Option c) E[u | X] = 0: This is the classic exogeneity assumption. It states that the conditional mean of the error term given X is zero, meaning the errors reveal no systematic information about X. Under this assumption (along with other standard Gauss-Markov conditions like linearity, no perfect multicollinearity, and homoscedasticity as needed), the OLS estimators are unbiased and consistent because E[bias-free terms] cancel out when taking expectations. This aligns with the fundamental requirement for unbiased OLS estimates in a simple regression.
Option d) Cov(X, u) ≠ 0: If the covariance between X and the error term is not zero, there is endogeneity, which biases the OLS estimates. This directly violates the exogeneity condition and leads to biased and inconsistent estimates, so this option describes the opposite of what is needed.
In summary, option c correctly captures the exogeneity condition required for OLS unbiasedness, while the other options correspond to properties that do not ensure unbiased estimation or even imply a problem (endogeneity) if violated.

Question1 Which OLS assumption guarantees that the OLS estimator is [math] in a simple linear regression? Select one alternative: a) [math] b) [math] c) [math] d) [math] ResetMaximum marks: 1 Flag question undefined

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