DOW vs the World

Every morning (when the markets aren't having a holiday), I check the Asian and European market indexes: http://money.cnn.com/data/premarket/ They're open before ours, eh? I'm hoping that I can tell whether North American markets will open Up or Down. Who influences whom? Of course, I've already investigated the possibilities: DOW vs the World ⊗ If foreign markets are Up (or Down) early one morning, will the DOW open Up (or Down) that day? ⊗ If the DOW closes Up (or Down) one day, will foreign markets open Up (or Down) the next day? Alas, I never learn! I can't tell nothin' from foreign markets.