Question

Given a set of n data points, (x1,y1),(x2,y2),…,(xn,yn), the best least squares fit f(x) is obtained by minimization of:
∑ni=1[yi−f(xi)]
min(yi−f(xi))
∑ni=1[yi−f(xi)]2
max(yi−f(xi))

Answer 1

∑n(i)=1[y(i)−f(xi)]2.

Answer 2

The best least squares fit f(x) is obtained by minimization of ∑ni = 1[yi-f(xi)]^2.

• Let the magnitude of residual be Ai at every n data points.
• Then, Ai = yi-f(xi),i = 1, 2, 3,......,n-1, n. Here, n are the data points.
• Practically, it is impossible for all residuals Ai are zero if all points found in an equation lie on the model. But, this is ideally possible.
• The least squares method is the most popular method to minimize the residual.
• In this method, the constants of the models are chosen in such a way that the sum of the squares residuals is minimized.

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