What's the error of numpy.polyfit?

Question

I want to use numpy.polyfit for physical calculations, therefore I need the magnitude of the error.

Answer 1

If you specify full=True in your call to polyfit, it will include extra information:

>>> x = np.arange(100)
>>> y = x**2 + 3*x + 5 + np.random.rand(100)
>>> np.polyfit(x, y, 2)
array([ 0.99995888,  3.00221219,  5.56776641])
>>> np.polyfit(x, y, 2, full=True)
(array([ 0.99995888,  3.00221219,  5.56776641]), # coefficients
 array([ 7.19260721]), # residuals
 3, # rank
 array([ 11.87708199,   3.5299267 ,   0.52876389]), # singular values
 2.2204460492503131e-14) # conditioning threshold

The residual value returned is the sum of the squares of the fit errors, not sure if this is what you are after:

>>> np.sum((np.polyval(np.polyfit(x, y, 2), x) - y)**2)
7.1926072073491056

In version 1.7 there is also a cov keyword that will return the covariance matrix for your coefficients, which you could use to calculate the uncertainty of the fit coefficients themselves.