Answer: Find a system of equations whose solution yields the coefficients and for the

Chapter 13, Problem 37

(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), ldots , (x_n, y_n)

S(a, b, c) = sum_i=1 ^n (y_i - ax_i ^2 - bx_i - c)^2