Finding the Least-Squares Curve Let {be a set of N points,where the abscissas are distinct.The least-squares curve yfx)is the best one in some function class that minimizes the root-mean-square error E2(f). The simplest formula is the line y-fx)=Ax+B. The quantity E2(f)will be a minimum if and only if the quantity (E((+B-)is a minimum The latter is visualized geometrically by minimizing the sum of the squares of the vertical distances from the points to the line.Finding the Least-Squares Curve ◼ Let {(𝑥𝑘, 𝑦𝑘)}𝑘=1 𝑁 be a set of N points, where the abscissas {xk} are distinct. The least-squares curve y=f(x) is the best one in some function class that minimizes the root-mean-square error E2 (f ). ◼ The simplest formula is the line y=f(x)=Ax+B. ◼ The quantity E2 (f ) will be a minimum if and only if the quantity is a minimum. ◼ The latter is visualized geometrically by minimizing the sum of the squares of the vertical distances from the points to the line. 2 2 2 1 ( ( )) ( ) N k k k N E f Ax B y = = + − 