Can we remove significant variables in a regression? I first ran a regression with all the variables and then ran the regression again with only significant variables (or the variables of interest).
One of the variables in the 2nd regression is highly correlated with another variable of interest, though both of them are significant but are highly correlated. And this is causing the sign of the coefficient of other variables to go opposite way (not as per expectation or theory).
My question is that can we still remove one of those (correlated) significant variables? It makes the whole result come as per the expectations.
Thanks

To just address the actual question: Significance means that there is evidence that the variable has a nonzero contribution given all other variables in the model. This means that correlation is not a valid reason to remove a significant variable, because its significance means that its contribution can not be accounted for by the other variable.
Otherwise I agree regarding the critical remarks on variable selection based on p-values in general. The Lasso may be better here. Also, if you choose analyses based on what you expect from theory, your analyses will be invalid because you bias them in order to fit your theory.
