How to use least squares with weight matrix?

Question

I know how to solve A.X = B by least squares using Python:

Example:

A=[[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,0,0]]
B=[1,1,1,1,1]
X=numpy.linalg.ls         


        

Answer 1

scikit package offers weighted regression directly .. https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression.fit

import numpy as np
# generate random data
N = 25
xp = [-5.0, 5.0]
x = np.random.uniform(xp[0],xp[1],(N,1))
e = 2*np.random.randn(N,1)
y = 2*x+e
w = np.ones(N)

# make the 3rd one outlier
y[2] += 30.0
w[2] = 0.0

from sklearn.linear_model import LinearRegression
# fit WLS using sample_weights
WLS = LinearRegression()
WLS.fit(x, y, sample_weight=w)

from matplotlib import pyplot as plt
plt.plot(x,y, '.')
plt.plot(xp, xp*WLS.coef_[0])
plt.show()