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"""examples for usage of F-test on linear restrictions in OLS
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linear restriction is R \beta = 0
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R is (nr,nk), beta is (nk,1) (in matrix notation)
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import numpy.testing as npt
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from models.datasets.longley.data import load
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from models.regression import OLS
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from models import tools
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data.exog = tools.add_constant(data.exog)
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res = OLS(data.endog, data.exog).fit()
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# test pairwise equality of some coefficients
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R = [[0,1,-1,0,0,0,0],[0, 0, 0, 0, 1, -1, 0]]
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Ftest = res.Fcontrast(R)
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print repr((Ftest.F, Ftest.p_val)) #use repr to get more digits
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# 9.740461873303655 0.0056052885317360301
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##Compare to R (after running R_lm.s in the longley folder) looks good.
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##> linear.hypothesis(m1, c("GNP = UNEMP","POP = YEAR"))
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##Linear hypothesis test
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##Model 1: TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR
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##Model 2: restricted model
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## Res.Df RSS Df Sum of Sq F Pr(>F)
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##2 11 2646903 -2 -1810479 9.7405 0.005605 **
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# test all variables have zero effect
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Ftest0 = res.Fcontrast(R)
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print repr((Ftest0.F, Ftest0.p_val))
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npt.assert_almost_equal(res.F, Ftest0.F, decimal=10)
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# values differ in 11th decimal
b'\\ No newline at end of file'
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nipy/fixes/scipy/stats/models/examples/ols_fstat.py
