But now apart from the law the righteousness of God has been made known, to which the Law and the Prophets testify. This righteousness is given through faith in Jesus Christ to all who believe. There is no difference between Jew and Gentile, for all have sinned and fall short of the glory of God, and all are justified freely by his grace through the redemption that came by Christ Jesus.
Least-squares solutions techniques are used when a system has no actual solution; that is, the situation where a system is inconsistent. In this case, we find an object that is the closest to being a solution among all possibilities. This object minimizes the value of the distance between the transformation of the object and the impossible result.
In our lives we must solve an impossible problem--we must perfectly meet the entire law of God if we are to have eternal life. No matter how hard we try, we are unable to do this. Fortunately, God loves us so much that he sent his Son Jesus to solve the problem for us. Christ took upon himself our sin and gave his life so that we might live. Jesus is our least-squares solution to the impossible problem. Note, though, that the distance between us and the law of God is infinite; through salvation in Christ, God accepts us as if the error is zero!