I'm a beginner in econometrics (learning on my own, and not from school) and I'm trying to build an intuition to understanding linear regression. We know that modeling real world data is bound to break many of the rules surrounding linear regression. Does it mean breaking any of those rules would render the use of linear regression ineffective? Or should we test the materiality of breaking those rules. How do we go about testing the materiality? Otherwise, what alternatives should we use?
The assumptions underlying linear regression states that:
Expected value of the error term, conditional on the independent variable, is zero. Qn: What happens if it's not zero, how do you test for it, and when is it considered significant?
All x, y observations are i.i.d. Qn: How would that affect my regression results if they weren't?
It is unlikely that large outliers will be observed in the data. Qn: What should you do if large outliers are observed? should you ignore those data points? if yes, how would you know those data points can be ignored?
Independent variable is uncorrelated with the error terms Qn: How do you test for this correlation, and are there ways to mitigate this correlation?
Homoskedasticity Qn: what if the variance of the error term is not constant? What should you do?