Exercise "Least-squares fit"

1. Make a function/subroutine that fits a given data-set [x_i, y_i, σ_i, i=1..n] with a linear combination of given functions [f_k(x), k=1..m]. The function/subroutine must return the vector of coefficients and the covariance matrix.
2. Make a linear fit to the following data

   xi = i+1/2, yi = i + cos(2i), σi = 1+sin2(2i), i=0..10

3. Make some other interesting fits.