Exercise "Least-squares fit"

1. Make a 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 subroutine must return the vector of coefficients and the covariance matrix.
2. Make some interesting fits, e.g. investigate how reasonable the errors on the fitting coefficients are.