Chapter 5.3, Problem 7E

Given a collection of points $\left(x_1,y_1\right),\left(x_2,y_2\right),...,\left(x_n,y_n\right),$ let
$\begin{array}{l}x={\left(x_1,x_2,...,x_n\right)}^{T}y={\left(y_1,y_2,...,y_n\right)}^T\\ \bar{x}=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{\sum }}{x}_i\bar{y}=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{\sum }}{y}_i}}\end{array}$

and let $y=c_0+c_{1}x$ be the linear function that gives the best least squares fit to the points. Show that if $\bar{x}=0,$ then
$c_0=\bar{y}$ and $c_1=\frac{x^{T}y}{x^{T}x}$