Soluting the Normal Equations The normal equations may be an ill-conditioned linear system. The coefficients 4 and B for the least-squares line can be computed as follows.First compute the means and y,and then perform the calculations: C=立4-明，42x-0y-0B=-在 The algorithm aboved is computationally stable.It gives reliable results in cases when the normal equations are ill-conditioned.Soluting the Normal Equations ◼ The normal equations may be an ill-conditioned linear system. ◼ The coefficients A and B for the least-squares line can be computed as follows. First compute the means 𝑥ҧand 𝑦ത, and then perform the calculations: ◼ The algorithm aboved is computationally stable. It gives reliable results in cases when the normal equations are ill- conditioned. 2 1 1 1 ( ) , ( )( ), N N k k k k k C x x A x x y y B y Ax = = C = − = − − = −  