Note that in this one verse the Holy Spirit is called both "the Spirit of God" and "the Spirit of Christ." Thus the two terms are synonymous, which means that Christ is God, and so is the Holy Spirit.
Note also that we "have received the Spirit of adoption, whereby we cry, Abba, Father" (Romans 8:15). In fact, our text assures each of us that we are actually living "in the Spirit," because He has come to "dwell in you." All of this has come about "not by works of righteousness which we have done, but according to his mercy, . . . by the washing of regeneration, and renewing of the Holy Ghost" (Titus 3:5). This glorious new birth, with sins forgiven and eternal life, is accomplished by the Holy Spirit in response to our faith in Christ as Savior and Lord.
But also note that "if any man have not the Spirit of Christ, he is none of his." It is absolutely vital that we have the Holy Spirit, "for as many as are led by the Spirit of God, they are the sons of God" (Romans 8:14). The question is, just how do we know that we have the Holy Spirit?
The answer is, because His Word says so! "He that heareth my word, and believeth on him that sent me," said Jesus, "hath everlasting life" (John 5:24). Furthermore, we have the testimony of internal peace and assurance. "The Spirit |Himself| beareth witness with our spirit, that we are the children of God" (Romans 8:16).
Finally, the indwelling Spirit will increasingly be growing His eternal fruit in our lives--the ninefold fruit of "love, joy, peace, longsuffering, gentleness, goodness, faith, meekness, temperance" (Galatians 5:22-23), and this will testify to others also that we do indeed have the Holy Spirit. HMM http://www.icr.org/article/5986/