Method of Least Squares Find a system of equations whose solution yields the

Chapter 13, Problem 31

(choose chapter or problem)

Find a system of equations whose solution yields the coefficients a, b and c for the least-squares regression quadratic

\(y=a x^{2}+b x+c\)

for the points \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right), \ldots,\left(x_{n}, y_{n}\right)\) by minimizing the sum

\(S(a, b, c)=\sum_{i=1}^{n}\left(y_{i}-a x_{i}^{2}-b x_{i}-c\right)^{2}\) .

Text Transcription:

y = ax^2 + bx + c

(x_1, y_1), (x_2, y_2), … , (x_n, y_n)

S(a, b, c) = sum_{i = 1}^n (y_{i} - ax_{i}^{2} - bx_{i} - c)^2