class statsmodels.regression.linear_model.WLS(endog, exog, weights=1.0, missing='none', hasconst=None, **kwargs)[source]

A regression model with diagonal but non-identity covariance structure.

The weights are presumed to be (proportional to) the inverse of the variance of the observations. That is, if the variables are to be transformed by 1/sqrt(W) you must supply weights = 1/W.


1-d endogenous response variable. The dependent variable.


A nobs x k array where nobs is the number of observations and k is the number of regressors. An intercept is not included by default and should be added by the user. See

weightsarray-like, optional

1d array of weights. If you supply 1/W then the variables are pre- multiplied by 1/sqrt(W). If no weights are supplied the default value is 1 and WLS results are the same as OLS.


Available options are ‘none’, ‘drop’, and ‘raise’. If ‘none’, no nan checking is done. If ‘drop’, any observations with nans are dropped. If ‘raise’, an error is raised. Default is ‘none.’

hasconstNone or bool

Indicates whether the RHS includes a user-supplied constant. If True, a constant is not checked for and k_constant is set to 1 and all result statistics are calculated as if a constant is present. If False, a constant is not checked for and k_constant is set to 0.

See also



If the weights are a function of the data, then the post estimation statistics such as fvalue and mse_model might not be correct, as the package does not yet support no-constant regression.


>>> import numpy as np
>>> import statsmodels.api as sm
>>> Y = [1,3,4,5,2,3,4]
>>> X = range(1,8)
>>> X = sm.add_constant(X)
>>> wls_model = sm.WLS(Y,X, weights=list(range(1,8)))
>>> results =
>>> results.params
array([ 2.91666667,  0.0952381 ])
>>> results.tvalues
array([ 2.0652652 ,  0.35684428])
>>> print(results.t_test([1, 0]))
<T test: effect=array([ 2.91666667]), sd=array([[ 1.41224801]]), t=array([[ 2.0652652]]), p=array([[ 0.04690139]]), df_denom=5>
>>> print(results.f_test([0, 1]))
<F test: F=array([[ 0.12733784]]), p=[[ 0.73577409]], df_denom=5, df_num=1>

The stored weights supplied as an argument.


fit([method, cov_type, cov_kwds, use_t])

Full fit of the model.

fit_regularized([method, alpha, L1_wt, …])

Return a regularized fit to a linear regression model.

from_formula(formula, data[, subset, drop_cols])

Create a Model from a formula and dataframe.

get_distribution(params, scale[, exog, …])

Returns a random number generator for the predictive distribution.


The Hessian matrix of the model

hessian_factor(params[, scale, observed])

Weights for calculating Hessian


Fisher information matrix of model


Initialize (possibly re-initialize) a Model instance.


Returns the value of the gaussian log-likelihood function at params.

predict(params[, exog])

Return linear predicted values from a design matrix.


Score vector of model.


Whitener for WLS model, multiplies each column by sqrt(self.weights)