SwampThingPaul

N=60
mu=0
sd=2

np.random.seed(0)
ran = np.random.normal(size=N)
error1 = sd**2 * ran + mu
error2 = sd*.5 * ran + mu

lin = np.linspace(-15., 15., num=N)

SwampThingPaul

import numpy as np
from numpy.linalg import inv
import statsmodels.api as sm

# from scratch
x = sm.add_constant(x) # add constant in the 0 index
b = inv(x.T.dot(x)).dot(x.T).dot(y)
yest_ols = np.array([b[2]*v**2 + b[1]*v + b[0] for v in x.T[0]])

# with using numpy.linalg.lstsq

SwampThingPaul

import numpy.linalg as la
def tls(X,y):
    
    if X.ndim is 1: 
        n = 1 # the number of variable of X
        X = X.reshape(len(X),1)
    else:
        n = np.array(X).shape[1] 
    
    Z = np.vstack((X.T,y)).T

SwampThingPaul

import scipy.odr as odr

def odr_line(B, x):
    y = B[0]*x + B[1]*x**2
    return y

def perform_odr(x, y, xerr, yerr):
    quadr = odr.Model(odr_line)
    mydata = odr.Data(x, y, wd=1./xerr, we=1./yerr)
    #mydata = odr.Data(x, y)

SwampThingPaul

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
plt.style.use('ggplot')

fig, (ax1, ax2) = plt.subplots(ncols=2,figsize=(16,6))
plt.xlim((0, 10))
plt.ylim((0, 7))
plt.tight_layout(w_pad=1.5)
#red line