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# scikits.statsmodels.regression.WLS

class `scikits.statsmodels.regression.``WLS`(endog, exog, weights=1.0)

  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. Note that this is different than the behavior for GLS with a diagonal Sigma, where you would just supply W.

  Methods

  whiten
    Returns the input scaled by sqrt(W)

  Parameters: | endog : array-like n length array containing the response variabl exog : array-like n x p array of design / exogenous data weights : array-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 reults are the same as OLS.

  Notes

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

  Examples

      >>> import numpy as np
      >>> import scikits.statsmodels 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=range(1,8))
      >>> results = wls_model.fit()
      >>> results.params
      array([ 0.0952381 ,  2.91666667])
      >>> results.t()
      array([ 0.35684428,  2.0652652 ])
      <T test: effect=2.9166666666666674, sd=1.4122480109543243, t=2.0652651970780505, p=0.046901390323708769, df_denom=5>
      >>> print results.f_test([1,0])
      <F test: F=0.12733784321528099, p=0.735774089183, df_denom=5, df_num=1>

  Attributes

  weights | array | The stored weights supplied as an argument.
  See regression.GLS |  |

  Methods

  `fit`() | Full fit of the model.
  `hessian`(params) | The Hessian matrix of the model
  `information`(params) | Fisher information matrix of model
  `initialize`() |
  `loglike`(params) | Returns the value of the gaussian loglikelihood function at params.
  `predict`(exog[, params]) | Return linear predicted values from a design matrix.
  `score`(params) | Score vector of model.
  `whiten`(X) | Whitener for WLS model, multiplies each column by sqrt(self.weights)

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