linest.py

#reproduces the "stats" or "verbose" output from LINEST in Excel or Google Sheets

import numpy as np

data = np.genfromtxt('data.csv', delimiter=',', names=True)

x = data['x']
y = data['y']
n = len(y)
dofreedom = n-2

z, cov = np.polyfit(x,y,1,cov=True)
p = np.poly1d(z)
yp = p(x) #predicted y values based on fit
slope = z[0]
intercept = z[1]
r2 = np.corrcoef(x,y)[0][1]**2
regression_ss = np.sum( (yp-np.mean(y))**2)
residual_ss = np.sum( (y-yp)**2 )
slope_pm = np.sqrt(residual_ss / (dofreedom*np.sum((x-np.mean(x))**2)))
intercept_pm = slope_pm*np.sqrt(np.sum(x**2)/n)
s = np.sqrt(residual_ss/dofreedom)
F = regression_ss/s**2

print slope, intercept
print slope_pm, intercept_pm
print r2,s
print F, dofreedom
print regression_ss,residual_ss