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 and of the form . 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 coefficientsand.

Task 1:Construct an overdetermined system of equations of the form determining the vector ( meaning transposed).

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

-- the first part here is a 4x2 matrix, but my formatting is awful - sorry!

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 .

Task 3:Find and .

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!