Chapter 13.9, Problem 31E

EXPLORING CONCEPTS

Method of Least SquaresFind a system of equations whose solution yields the coefficients $a$, $b$, and $c$ for the least squares regression quadratic

$y=a{x}^2+bx+c$

for the points $(x_1,y_1),(x_2,y_2),\mathrm{...},(x_n,y_n)$ by minimizing the sum

$S(a,b,c)={\displaystyle \underset{i=1}{\overset{n}{\sum }}{(y_i-a{x}_i^2-b{x}_i-c)}^2.}$