code: def acorr_breusch_godfrey(res, nlags=None, store=False):
      """
      Breusch-Godfrey Lagrange Multiplier tests for residual autocorrelation.
  
      Parameters
      ----------
      res : RegressionResults
          Estimation results for which the residuals are tested for serial
          correlation.
      nlags : int, optional
          Number of lags to include in the auxiliary regression. (nlags is
          highest lag).
      store : bool, default False
          If store is true, then an additional class instance that contains
          intermediate results is returned.
  
      Returns
      -------
      lm : float
          Lagrange multiplier test statistic.
      lmpval : float
          The p-value for Lagrange multiplier test.
      fval : float
          The value of the f statistic for F test, alternative version of the
          same test based on F test for the parameter restriction.
      fpval : float
          The pvalue for F test.
      res_store : ResultsStore
          A class instance that holds intermediate results. Only returned if
          store=True.
  
      Notes
      -----
      BG adds lags of residual to exog in the design matrix for the auxiliary
      regression with residuals as endog. See [1]_, section 12.7.1.
  
      References
      ----------
      .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall;
        5th edition. (2002).
      """
  
      x = np.asarray(res.resid).squeeze()
      if x.ndim != 1:
          raise ValueError(
              "Model resid must be a 1d array. Cannot be used on"
              " multivariate models."
          )
      exog_old = res.model.exog
      nobs = x.shape[0]
      if nlags is None:
          nlags = min(10, nobs // 5)
  
      x = np.concatenate((np.zeros(nlags), x))
  
      xdall = lagmat(x[:, None], nlags, trim="both")
      nobs = xdall.shape[0]
      xdall = np.c_[np.ones((nobs, 1)), xdall]
      xshort = x[-nobs:]
      if exog_old is None:
          exog = xdall
      else:
          exog = np.column_stack((exog_old, xdall))
      k_vars = exog.shape[1]
  
      resols = OLS(xshort, exog).fit()
      ft = resols.f_test(np.eye(nlags, k_vars, k_vars - nlags))
      fval = ft.fvalue
      fpval = ft.pvalue
      fval = float(np.squeeze(fval))
      fpval = float(np.squeeze(fpval))
      lm = nobs * resols.rsquared
      lmpval = stats.chi2.sf(lm, nlags)
      # Note: degrees of freedom for LM test is nvars minus constant = usedlags
  
      if store:
          res_store = ResultsStore()
          res_store.resols = resols
          res_store.usedlag = nlags
          return lm, lmpval, fval, fpval, res_store
      else:
          return lm, lmpval, fval, fpval
  
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 9 for calling a global function with example usage: acorr_breusch_godfrey(res, nlags, store) and returns: lm,  lmpval,  fval,  fpval,  res_store, lm,  lmpval,  fval,  fpval