Brief code to calculate line of best fit for a single vector ('y'). Assumes the 'x' variable is a simple range from 0 .. N-1. Returns the intercept, the slope, the correlation between x and y, and the residual (error). Doesn't use the lstsq function in numpy but the results are the same.

linear_least_squares.py

import numpy
 
x = numpy.array(range(400))
xm = x.mean()
xstd = x.std()
 
def fitline(y):
    N = len(y)
    x = numpy.array(range(N))
    ym = y.mean()
    ystd = y.std()
    xm = x.mean()
    xstd = x.std()
    r = numpy.corrcoef(x, y)[0,1]
    b1 = r * (ystd / xstd)
    b0 = ym - (b1 * xm)
    resid = (y - numpy.array(x*b1)+b0) ** 2
    return b0, b1, r, resid.sum()