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Can I ignore multicolinearity problem if all the regression coefficients are highly significant?
My data is large enough (i.e. I have several regression models where each of the data points for them ranges from 2958 to 11646 data points for every each 6 independent variables. so it is 6 times of these 2958 - 11646 data points for each independent variable to count the total number of data points) and all the resulting coefficients are significant enough in less than 0.01 level. The only thing I see is that one of the variable has the correlation of 0.9 (i.e. the correlation value of one variable to another one is 0.9 but I do not want to remove either of them.).
I am trying to see on unit increase effect of this variable while keeping all other variables constant. Can I keep this variable?
Besides, if I delete one of the variable with high VIF which is between 13 anad 14, all the other VIF are safe but the intercept becomes insignificant for all cases
I am also referring to the following website comment: http://www.researchconsultation.com/multicollinearity-multiple-regression.asp
So, in sum, my ultimate goal is to use the final output from the logistic regression model generated from the independent variables and one binary dependent variable. If so, do you think I can ignore the multicolinearity problem?