Scipy.optimization linear function approximation

Question

I've looked at for function approximation methods in scipy.optimize and after reading description for functions figured out(maybe wrong) that they approximate non-linear functions only.

For instance if I've sample output after zip() function for x and y

[(1,1),(4,2),(6,4),(8,6),(10,11)]

As you can see, non-linear function approximates much better but I need linear for my purposes.

I admit the possibility that missed something in documentation of functions presented, so my apologize if question can be answered in the "read docs" way.

Answer 1

In addition to np.polyfit and scipy.stats.linregress as suggested by @user2589273, a low-level way to do linear regression is to solve for the matrix of coefficients using np.linalg.lstsq. Although this approach is a bit more work than using one of the pre-packaged functions for doing linear regression, it's very useful to understand how this works at a basic level, in particular when you start dealing with multivariate data.

For example:

import numpy as np

# a simple linear relationship: y = mx + c with m=0.5 and c=2
x = np.arange(50)
y = x * 0.5 + 2
y += np.random.randn(50) * 5    # add some noise

# we can rewrite the line equation as y = Ap, where A=[[x, 1]] and p=[[m], [c]]
A = np.c_[x, np.ones(50)]

# solving for p gives us the slope and intercept
p, residuals, rank, svals = np.linalg.lstsq(A, y)

Plotting the fit:

from matplotlib import pyplot as plt

fig, ax = plt.subplots(1, 1)
ax.hold(True)
ax.plot(x, y, 'ob', label='data')
ax.plot(x, A.dot(p), '-k', lw=2, label='linear fit')
ax.legend()