code: def compare_j(results_x, results_z, store=False):
      """
      Compute the J-test for non-nested models
  
      Parameters
      ----------
      results_x : RegressionResults
          The result instance of first model.
      results_z : RegressionResults
          The result instance of second model.
      store : bool, default False
          If true, then the intermediate results are returned.
  
      Returns
      -------
      tstat : float
          t statistic for the test that including the fitted values of the
          first model in the second model has no effect.
      pvalue : float
          two-sided pvalue for the t statistic
      res_store : ResultsStore, optional
          Intermediate results. Returned if store is True.
  
      Notes
      -----
      From description in Greene, section 8.3.3. Matches results for Example
      8.3, Greene.
  
      Tests of non-nested hypothesis might not provide unambiguous answers.
      The test should be performed in both directions and it is possible
      that both or neither test rejects. see Greene for more information.
  
      References
      ----------
      .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall;
         5th edition. (2002).
      """
      # TODO: Allow cov to be specified
      if _check_nested_results(results_x, results_z):
          raise ValueError(NESTED_ERROR.format(test="J comparison"))
      y = results_x.model.endog
      z = results_z.model.exog
      yhat_x = results_x.fittedvalues
      res_zx = OLS(y, np.column_stack((yhat_x, z))).fit()
      tstat = res_zx.tvalues[0]
      pval = res_zx.pvalues[0]
      if store:
          res = ResultsStore()
          res.res_zx = res_zx
          res.dist = stats.t(res_zx.df_resid)
          res.teststat = tstat
          res.pvalue = pval
          return tstat, pval, res
  
      return tstat, pval
  
imports: from statsmodels.compat.pandas import deprecate_kwarg
  from collections.abc import Iterable
  import numpy
  import pandas
  from scipy import stats
  from statsmodels.regression.linear_model import OLS, RegressionResultsWrapper
  from statsmodels.stats._adnorm import anderson_statistic, normal_ad
  from statsmodels.stats._lilliefors import kstest_exponential, kstest_fit, kstest_normal, lilliefors
  from statsmodels.tools.validation import array_like, bool_like, dict_like, float_like, int_like, string_like
  from statsmodels.tsa.tsatools import lagmat
label_desc: Use image node_id 4 for calling a global function with example usage: compare_j(results_x, results_z, store) and returns: tstat,  pval, tstat,  pval,  res