Comment on @rasbt's benchmark

lstsqr.py

def python_lstsqr(x, y):
    """ Computes the least-squares solution to a linear matrix equation. """
    len_x = len(x)
    x_avg = sum(x)/len_x
    y_avg = sum(y)/len(y)
    var_x = 0
    cov_xy = 0
    var_x = np.sum((x - x_avg)**2)
    cov_xy = np.sum((x - x_avg)*(y - y_avg))
    slope = cov_xy / var_x
    y_interc = y_avg - slope*x_avg
    return (slope, y_interc)

%%cython
import numpy as np
cimport numpy as np
cimport cython
@cython.boundscheck(False) 
@cython.wraparound(False)
cpdef cython_lstsqr(x_ary, y_ary):
    """ Computes the least-squares solution to a linear matrix equation. """
    cdef double x_avg, y_avg, var_x, cov_xy,\
         slope, y_interc, temp
    cdef double[:] x = x_ary # memory view
    cdef double[:] y = y_ary
    cdef long N
    cdef int i
    
    N = x.shape[0]
    x_avg = np.sum(x)/N
    y_avg = np.sum(y)/N
    var_x = 0
    cov_xy = 0
    for i in range(N):
        temp = (x[i] - x_avg)
        var_x += temp**2
        cov_xy += temp*(y[i] - y_avg)
    slope = cov_xy / var_x
    y_interc = y_avg - slope*x_avg
    return (slope, y_interc)