Omitted Variable Bias

This clip explains why omitting a relevant variable from a regression model will bias estimators for other, still included, variable coefficients.

[lastua]

Hello Ralf, I think there is a missing explanation here. At 2.39 everything shows up. We use the *true* y to find the covariance between x and y. Here, however, I do not see any relevancy of the estimated beta. To my understanding, beta tilde here gives one result which is based on the *true* model rather than the *estimated/biased* model. In an alternative setting, I could disregard the *estimated* model and get the same result for beta tilde, am I not right?

[humayeraislam]

Can you tell me, what happens when the explanatory variables are not correlated? Does the intercept term becomes unbiased as well due to the fact that the slope becomes unbiased?

[simranpanesar]

What about if the coefficients are negative?