Augmented Dickey-Fuller unit root test & cointegration

I have a pair of variables (x, y) over time. I want to regress y on x.

• Do I have to perform a ADF test 1st on x and y to find if both are stationary in their 1st difference (i.e. I(1))?
• What if they are non-stationary? Or 1 variable is stationary and the other isn't?

I am confused as to why I need to perform the ADF test and the implication of it. Correct me if I am wrong.

1. I think I am to perform ADF on x & y to find that both are I(1).
2. Next, perform a cointegration test to check if their linear combination is I(0), or stationary. If the conintegration test is I(0), it implies that the results of the regression of y on x is acceptable, as their linear combination is stationary.

So the next question is:

• How do I perform a cointegration test on the residuals? I am supposed to use the Levin, Lin and Chua (2002) test. But I understand that this test is a panel unit root test (xtunitroot), does it test for cointegration?

Note: I am using Stata 13.