Explanation

Omitted variable bias occurs when:

1. The omitted variable is correlated with the included regressor - This means the omitted variable and the included variable move together in some systematic way
2. The omitted variable is a determinant of the dependent variable - This means the omitted variable actually affects the outcome variable we're trying to predict

Why Option A is Correct:

• When both conditions are met, the estimated coefficient for the included variable becomes biased because it captures not only the true effect of the included variable but also part of the effect of the omitted variable
• This leads to incorrect inference about the relationship between the included variable and the dependent variable

Why Other Options are Incorrect:

• Option B: If the omitted variable is not a determinant of the dependent variable, omitting it doesn't cause bias
• Option C: If the omitted variable is independent of the included regressor, omitting it doesn't cause bias (though it may increase standard errors)
• Option D: If the omitted variable is independent and not a determinant, omitting it has no effect on bias

In econometrics, this is a fundamental concept in regression analysis where failing to include relevant variables that are correlated with included variables leads to biased coefficient estimates.