/Statsmodels

# statsmodels.regression.linear_model.OLSResults.t_test

`OLSResults.t_test(r_matrix, cov_p=None, scale=None, use_t=None)`

Compute a t-test for a each linear hypothesis of the form Rb = q

Parameters: r_matrix (array-like, str, tuple) – array : If an array is given, a p x k 2d array or length k 1d array specifying the linear restrictions. 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). If q is given, can be either a scalar or a length p 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) – An optional `scale` to use. Default is the scale specified by the model fit. use_t (bool, optional) – If use_t is None, then the default of the model is used. If use_t is True, then the p-values are based on the t distribution. If use_t is False, then the p-values are based on the normal distribution. res – The results for the test are attributes of this results instance. The available results have the same elements as the parameter table in `summary()`. ContrastResults instance

#### Examples

```>>> import numpy as np
>>> import statsmodels.api as sm
>>> results = sm.OLS(data.endog, data.exog).fit()
>>> r = np.zeros_like(results.params)
>>> r[5:] = [1,-1]
>>> print(r)
[ 0.  0.  0.  0.  0.  1. -1.]
```

r tests that the coefficients on the 5th and 6th independent variable are the same.

```>>> T_test = results.t_test(r)
>>> print(T_test)
Test for Constraints
==============================================================================
coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
c0         -1829.2026    455.391     -4.017      0.003   -2859.368    -799.037
==============================================================================
>>> T_test.effect
-1829.2025687192481
>>> T_test.sd
455.39079425193762
>>> T_test.tvalue
-4.0167754636411717
>>> T_test.pvalue
0.0015163772380899498
```

Alternatively, you can specify the hypothesis tests using a string

```>>> from statsmodels.formula.api import ols
>>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR'
>>> results = ols(formula, dta).fit()
>>> hypotheses = 'GNPDEFL = GNP, UNEMP = 2, YEAR/1829 = 1'
>>> t_test = results.t_test(hypotheses)
>>> print(t_test)
Test for Constraints
==============================================================================
coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
c0            15.0977     84.937      0.178      0.863    -177.042     207.238
c1            -2.0202      0.488     -8.231      0.000      -3.125      -0.915
c2             1.0001      0.249      0.000      1.000       0.437       1.563
==============================================================================
```