Minimizing least squares regression?

Consider fitting the data {(1, 4),(3, 5),(5, −2)} with the curve f(x) = c1x+c2 so that f(x) minimizes the least squares error This task can also be expressed in A*x = ~b form, where x = [c1, c2] Find A.

I don't need to use matlab to do this one... but i still dont understand how to find A...

Answer 1

[Star Strider]

The generic representation A*x = b may seem a bit confusing. You create ‘A’ from the independent variable, and estimate parameter vector ‘x’ from ‘A’ and ‘b’, the dependent variable. The documentation for mldivide,\ goes into detail on the solution to this and the algorithms it uses, so I’ll spare you my description.

Answer 2

[Torsten]

The function to be minimized is

F(c1,c2) = (c1*1+c2-4)^2 + (c1*3+c2-5)^2 + (c1*5+c2-(-2))^2

To find the minimum, you will have to form the partial derivatives with respect to c1 and c2 and set them to zero.

After you've done this, you'll find the A and b in your equation from above.

Best wishes

Torsten.