How to solve this best least squares fit problem
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 coefficients and .
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!