No, regeneration is not by the indwelling of the Holy Spirit. The indwelling is a result of regeneration.
Rom 6:1-7 shows that the The Holy Spirit removes our sins and then He resurrects us, just as Jesus died and then was resurrected.
Sorry you provided nothing to show that.
Instead you ignored both scripture and systematic theology
John 7:38 (KJV 1900) — 38 He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water.
John 4:14 (KJV 1900) — 14 But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life.
Regeneration. A biblical motif of salvation that emphasizes the rebirth or re-creation of fallen human beings by the indwelling Holy Spirit. One central biblical text depicting salvation as regeneration is Jesus’ conversation with Nicodemus in which he emphasized the necessity of being “born again” (Jn 3:1–21). Pocket dictionary of Theological terms
The perfect tense “has given” denotes the resultant indwelling of the Spirit imparted at regeneration. In 3:24 use of the aorist tense asserted the historical
Bibliotheca Sacra: A Quarterly Published by Dallas Theological Seminary (Dallas, TX: Dallas Theological Seminary, 1955–1995).
The Holy Spirit applies the benefits of salvation to those whom he indwells. The indwelling of the Spirit is both corporate and individual; Christ’s church is his temple, as are individual Christians. In regeneration, the Spirit gives new life to the believer, birthing a new creation.
Susanne Calhoun, “The Spirit’s Indwelling,” in Lexham Survey of Theology (ed. Mark Ward et al.; Bellingham, WA: Lexham Press, 2018).
Regeneration. That mighty work of the Holy Spirit of God whereby one is “delivered out of the power of darkness and translated into the kingdom of the Son of his love” (Col. 1:13; comp. 1 Pet. 2:9) is spoken of in John 3:5–8, as being “born of the Spirit.” Whosoever is thus begotten of God is conceived as a “new creation” (2 Cor. 5:17; Gal. 6:15), “created in Christ Jesus for good works” (Eph. 2:10), “the new man, who after God hath been created in righteousness and holiness of truth” (Eph. 4:24). This mighty change is also conceived as being raised from the dead so as to “walk in newness of life” (Rom. 6:4); and even the quickening of our mortal bodies into the resurrection life is through the power of the indwelling Spirit (Rom. 8:11)
Milton S. Terry, Biblical Dogmatics: An Exposition of the Principal Doctrines of the Holy Scriptures (New York; Cincinnati: Eaton & Mains; Jennings & Graham, 1907), 499.
Regeneration is the divine action by which God renews the fallen creation so that it reflects his character.
For human beings, regeneration is the answer to the corruption of moral character caused by sin. It is essential for participation in the kingdom of God (John 3:3). At conversion, God grants the believer new life and a new identity in Christ. This event is so powerful that John refers to it as a new birth, a birth “from above” (John 3:3), while Paul refers to it as a “new creation” (2 Cor 5:17). In either case, the change is brought about by the Holy Spirit, who comes to indwell the believer.
Brenda B. Colijn, “Regeneration,” in Lexham Survey of Theology (ed. Mark Ward et al.; Bellingham, WA: Lexham Press, 2018).