Good morning Jackson 123, Sorry I did not get back to you yesterday on this but I was working.
To answer your question: Yes there is an absolute correlation between faith and a Holy life.
If I believe in Jesus Christ, then I believe in what Jesus Christ believes, which is to Love God and our neighbors.
To love God and our neighbor are spiritual qualities that make one holy.
If I do love God, I would attempt to do what would please God, the first of these being to offer myself a living sacrifice by leaving my worldly carnal inclinations behind me. I would then be holy before the Lord, and acceptable (Romans 12:1). If I did not do this most basic reasonable service, I would then be carnally inclined and conformed to the world (Romans 12:2), which is enmity to the spirit (Romans 8:7).
Romans 12:1 I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service. 2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
Romans 8:7 Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.