Question on omission error regarding regression equations:
The book says “If a specific independent variable is correlated with the remaining independent variables, then the error terms will also be correlated with the same independent variables and the resulting regression coefficients are biased and inconsistent”
Does this imply if x1 is correlated with the other independent variable x2, then if x1 was omitted from the regression equation the coefficient estimates would be inaccurate due to the fact that x2 is also correlated with the error term, since its correlated with x1.
This does not make sense to me. Is this a problem of multcollinearity? How so?
I just do not get how ommitting one x variables means that the other variables are correlated with the residuals. It is basically saying: “If x1 is correlated with any of the remaining independent variables, then the error term is also correlated with the same independent variables and th resulting regression coefficients are biased and inconsistent”
Not sure if I am reading too much into this but I just do not get how they jump from statement 1 to statement 2.
The error term “absorbs” anything not specified in the model. It can include variables we could have included but did not. Therefore, if X1 is correlated with X2, and you omit X2 from the model, it is “absorbed” into the error term. The error term is then correlated with X1 because X2 is included in the error.