I have two problems:
1) I have a regression coefficient that is very significant (large dataset), but has low practical significance. Can I say there is no relationship? And I mean really tiny, like .000005.
2) I have a specific question about my project. So I am regressing "terrorist attacks" to "internet use" to see if being in a "high internet access area" relates to local terrorism. However, I feel like I should control for "stability," since that presents a fairly likely confounder. But when I control for it, the sign of the internet coefficient switches due to multicollinearity. I'm not sure about the relative trade-offs of including it or not. Whats your advice?
Definitions: attacks - attack count per country per year
internet access - proportion of population with internet access per country per year
stability - an index from the Failed States Index