# How Does Adding Regressors Affect Standard Errors and Existing Coefficients?

(First off, bonus points if you can write my question title more clearly)

My project right now is to research citizenship status and income.

At first my regression was like this:

$$INCOME = \beta0 + \beta1STATUS$$

Now, I am going to do one with control variables like this: $$INCOME = \beta0 + \beta1STATUS + \beta2EDUCATION + \beta3ZIPCODE$$ When I'm looking at the coefficient and standard error for immigration status, what does the regression of earnings on immigration status and all my control variables tell me compared to a regression of just earnings on immigration status? Generally in regressions, how does adding more variables change standard errors and coefficients?

• As far as your question about coefficients, this question has been answered here: stats.stackexchange.com/questions/52067/… – DornerA Mar 25 '16 at 23:13
• And for your question about standard errors, it is answered here: stats.stackexchange.com/questions/97179/… – DornerA Mar 25 '16 at 23:17
• The correct answer is that it depends. What's most likely going to happen in your case though is that the standard errors will go up and the coefficient will go down. – BB King Mar 26 '16 at 0:21
• Whoever fixed my title question, here's some bonus points. +1,000,000! – user4207 Mar 26 '16 at 16:14
• @DornerA, those helped so much! Thank you! – user4207 Mar 26 '16 at 16:16