How to solve this best least squares fit problem

Hello,

I find myself needing to solve a number of best least squares fit problems, and honestly I don't remember the specifics of how it's done. Therefore I'm trying to nail the solution to a single problem before moving on with the rest - and I'd really like some help with that. Here's the description:

*It is assumed that there is a coherence between the variables $\displaystyle x$ and $\displaystyle y$ of the form $\displaystyle y=c0+c1*x$. Given the following data (table)*

x -1 1 2 4

y 0 1 3 4

we wish to find the best possible values for the coefficients $\displaystyle c0$* and *$\displaystyle c1$*.*

**Task 1:** Construct an overdetermined system of equations of the form $\displaystyle A*c=y$ determining the vector $\displaystyle c=(c0,c1)^T$ ($\displaystyle ^T$ meaning transposed).

I immediately imagine the answer to this is simply the following table:

$\displaystyle -1$ $\displaystyle 0$

$\displaystyle 1$ $\displaystyle 1$

$\displaystyle ( 2$ $\displaystyle 3 ) * ( x$ $\displaystyle y )^T = ( c0$ $\displaystyle c1 )^T$ -- the first part here is a 4x2 matrix, but my formatting is awful - sorry!

$\displaystyle 4$ $\displaystyle 4$

But that doesn't seem to match the required form. What is the correct answer - and why?

Furthermore, I'm most uncertain as to how the following tasks are solved...

**Task 2:** Calculate the normal equations $\displaystyle A^T*A*c=A^T*y$.

**Task 3:** Find $\displaystyle c0$ and $\displaystyle c1$.

Could someone explain how it's done? I could really use some help as I pretty much don't have a clue here.

Lots of thanks!