# statsmodels.duration.hazard_regression.PHRegResults.f_test¶

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

Compute the F-test for a joint linear hypothesis.

This is a special case of wald_test that always uses the F distribution.

Parameters: r_matrix : array-like, str, or tuple array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero. str : The full hypotheses to test can be given as a string. See the examples. tuple : A tuple of arrays in the form (R, q), `q` can be either a scalar or a length k row vector. cov_p : array-like, optional An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used. scale : float, optional Default is 1.0 for no scaling. invcov : array-like, optional A q x q array to specify an inverse covariance matrix based on a restrictions matrix. res : ContrastResults instance The results for the test are attributes of this results instance.

Notes

The 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.

Examples

```>>> import numpy as np
>>> import statsmodels.api as sm
>>> 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.fvalue
330.2853392346658
>>> results.f_pvalue
4.98403096572e-10
```
```>>> B = np.array(([0,0,1,-1,0,0,0],[0,0,0,0,0,1,-1]))
```

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>
```

Alternatively, you can specify the hypothesis tests using a string

```>>> from statsmodels.datasets import longley
>>> from statsmodels.formula.api import ols