Ok, here are two regression problems that the CFA text outlines that seem to contradict each other: Multicollinearity: occurs when two or more independent variables are highly (but not perfectly) correlated with each other. Does not effect consistency of the estimates of the coefficients, but estimates become unreliable. Solution: drop one of the variables. Ommited Variable Bias: “if an ommited variable is correlated with variables already included in the model, coefficient estimates will be biased and inconsistent and standard errors will aslo be inconsistent” So, if I include the variable I run the risk of Multicollinearity, if I don’t then I have ommited variable bias. What are you suppost to do?

if you want to pull a variable out you need to restate the model

yes and then I have ommited variable bias. If the ommited variabel (x2) is correlated with the remaining variable (x1) and the estimated values of the regression coefficients would be biased and inconsistent. Also the estimates of the std errors of those coeffic will aslo be inconsistent so cant use the coeffic or the std errors.

that is why omitting a variable is not good even if the variable is not relevant if you want to omit the variable you need a NEW model if you want to use the old one you need to adjust for errors but include the insignificant variable

what? if i include a variable that is not relevant then my model is mispecified. I have to confirm that the intercept and coefficients are reasonable to include by using the t test. If it is not significant then I can’t use that variable. Also if two independent variables are correlated with each other I have multiple collinearity, which the proper recourse is to ommit the variable and run a NEW model. However, if I dont include the variable I have misspecified the model by Ommited Variable Bias