linear regression with multiple regressors?

Question 1

what are two conditions for which omitted variables bias occurs?

Answer 1

1) the omitted variable is correlated with the included regressor
2) the committed variable is a determinant of the dependent variable

Both conditions must hold for the omission of Z to result in omittedvariable bias.

Question 2

what is ommitted variable bias?

Answer 2

it is the bias in the OLS estimator of the causal effect of X on Y that arises when the regressor X is correlated with an omitted variable