Least square fit a 2D line
I realize I could use numpy to find the line like so:
import numpy as np import matplotlib.pyplot as plt a = np.array([1,2,3,4,6,7]) b = np.array([5,4,3,2,-2,-1]) k,m = np.polyfit(a,b,1) plt.scatter(a,b) plt.plot([0,10],[m,10*k+m]) plt.show()
but I'd like to use raw python code instead. My math is too rusty, but if can be done in a few lines of code I'd really appreciate the help!
If you are looking for a simple linear regression based on minimizing the quadratic error, the pure Python implementation is pretty straightforward (check equations for α and β on the link above):
def linear_fit(x, y): """For set of points `(xi, yi)`, return linear polynomial `f(x) = k*x + m` that minimizes the sum of quadratic errors. """ meanx = sum(x) / len(x) meany = sum(y) / len(y) k = sum((xi-meanx)*(yi-meany) for xi,yi in zip(x,y)) / sum((xi-meanx)**2 for xi in x) m = meany - k*meanx return k, m
For your sample input:
>>> x = [1,2,3,4,6,7] >>> y = [5,4,3,2,-2,-1] >>> linear_fit(x, y) (-1.1614906832298135, 6.285714285714285)