Homework 4, Math 152-205, additional problem:

Given the model y(x) = a + b x, the least squares fit to the data
to the n data (x1,y1), (x2,y2), ..., (xn,yn) is given by the values
of  a  and  b  with

[       n         x1+...+xn      ]  [ a ]     [    y1+...+yn        ]
[                                ]  [   ]  =  [                     ]
[  x1+...+xn   (x1)^2+...+(xn)^2 ]  [ b ]     [ x1 y1 + ... + xn yn ]

(See the Froese-Wetton notes, Problem 4.44, or 
http://mathworld.wolfram.com/LeastSquaresFitting.html, equation (9), or
just type "Least Squares" or "Polynomial Least Squares" into an internet search
engine.)

Derive the equations you would get for  a,b,c  with the model
y(x) = a + b x + c x^2.  Explain this using the formulation of least
squares in the notes (where the best approximation to solving B x = c
is given by the "normal equations" B^T B x = B^T c ; here x,c are
different from the x,c above).