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# scikits.statsmodels.glm.GLMResults.f_test

`GLMResults.``f_test`(r_matrix, scale=1.0, invcov=None)

  Compute an Fcontrast/F-test for a contrast matrix.

  Here, matrix r_matrix is assumed to be non-singular. More precisely,

  r_matrix (pX pX.T) r_matrix.T

  is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full.

  Parameters: | r_matrix : array-like q x p array where q is the number of restrictions to test and p is the number of regressors in the full model fit. If q is 1 then f_test(r_matrix).fvalue is equivalent to the square of t_test(r_matrix).t scale : float, optional Default is 1.0 for no scaling. invcov : array-like, optional A qxq matrix to specify an inverse covariance matrix based on a restrictions matrix.

  See also

  `scikits.statsmodels.contrasts`, `scikits.statsmodels.model.t_test`

  Examples

      >>> import numpy as np
      >>> import scikits.statsmodels as sm
      >>> data = sm.datasets.longley.Load()
      >>> data.exog = sm.add_constant(data.exog)
      >>> results = sm.OLS(data.endog, data.exog).fit()
      >>> A = np.identity(len(results.params))
      >>> A = A[:-1,:]

  This tests that each coefficient is jointly statistically significantly different from zero.

      >>> print results.f_test(A)
      <F contrast: F=330.28533923463488, p=4.98403052872e-10, df_denom=9, df_num=6>

  Compare this to

      >>> results.F
      330.2853392346658
      >>> results.F_p
      4.98403096572e-10

      >>> B = np.array(([0,1,-1,0,0,0,0],[0,0,0,0,1,-1,0]))

  This tests that the coefficient on the 2nd and 3rd regressors are equal and jointly that the coefficient on the 5th and 6th regressors are equal.

      >>> print results.f_test(B)
      <F contrast: F=9.740461873303655, p=0.00560528853174, df_denom=9, df_num=2>

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