Python code of WLS

WLS (Weighted Least Squares) is a method used to estimate the parameters of a linear regression model when the errors are heteroscedastic (i.e., the variance of the errors is not constant). Here is an example Python code of WLS:

import numpy as np
import statsmodels.api as sm

# Generate some data
x = np.arange(10)
y = 2*x + 5 + np.random.normal(0, 1, 10)  # Heteroscedastic errors

# Fit a linear regression model using WLS
weights = 1 / np.arange(1, 11)  # Weights are inversely proportional to x
X = sm.add_constant(x)
model = sm.WLS(y, X, weights=weights)
results = model.fit()

# Print the results
print(results.summary())

In this example, we generate some data with heteroscedastic errors and fit a linear regression model using WLS. The weights are chosen to be inversely proportional to x (i.e., higher weights are assigned to smaller values of x), which is a common choice in practice. The `sm.WLS` function from the `statsmodels` library is used to perform the WLS estimation, and the results are printed using the `summary` method of the `results` object.