Regeneration, (Greek: παλιγγενεσία, palingenesia) is a word only found in Matt. 19:28 and Titus 3:5, but it can be used to define what Scripture describes elsewhere using other words. The word literally means a “new birth.” In Matt. 19:28 the word is used by Jesus to describe the new heavens and the new earth, translated “new world.” In Titus 3:5 it is used to describe the change of heart described in Romans 12:2, or elsewhere spoken in Scripture as a passing from death to life (1 John 3:14); becoming a new creature in Christ Jesus (2 Cor. 5:17); being born again (John 3:5); a resurrection from the dead even before our physical death (Eph. 2:6); and a being quickened or “made alive” (Ephesians 2:1,5).
So does this regeneration precede faith? The answer is yes. But to further explain, today I’d like to share a well written article by someone else. (Thomas R. Schreiner, on the 9 Marks site)
 These are my own words, but I consulted with the original Greek, the LSJ dictionary, and Easton, M. G. (1893). In Illustrated Bible Dictionary and Treasury of Biblical History, Biography, Geography, Doctrine, and Literature (p. 577). New York: Harper & Brothers.