code: def test_HC_use():
      np.random.seed(0)
      nsample = 100
      x = np.linspace(0, 10, 100)
      X = sm.add_constant(np.column_stack((x, x**2)), prepend=False)
      beta = np.array([1, 0.1, 10])
      y = np.dot(X, beta) + np.random.normal(size=nsample)
  
      results = sm.OLS(y, X).fit()
  
      # test cov_params
      idx = np.array([1, 2])
      cov12 = results.cov_params(column=[1, 2], cov_p=results.cov_HC0)
      assert_almost_equal(
          cov12, results.cov_HC0[idx[:, None], idx], decimal=15
      )
  
      # test t_test
      tvals = results.params / results.HC0_se
      ttest = results.t_test(np.eye(3), cov_p=results.cov_HC0)
      assert_almost_equal(ttest.tvalue, tvals, decimal=14)
      assert_almost_equal(ttest.sd, results.HC0_se, decimal=14)
  
      # test f_test
      ftest = results.f_test(np.eye(3)[:-1], cov_p=results.cov_HC0)
      slopes = results.params[:-1]
      idx = np.array([0, 1])
      cov_slopes = results.cov_HC0[idx[:, None], idx]
      fval = np.dot(
          slopes, np.dot(np.linalg.inv(cov_slopes), slopes)
      ) / len(idx)
      assert_allclose(ftest.fvalue, fval, rtol=12)
  
imports: import numpy
  from numpy.testing import assert_almost_equal, assert_allclose
  import statsmodels.api
label_desc: Use image node_id 1 for calling a global function with example usage: test_HC_use() without return types