code: def process_intercept(x, beta, intercept, pred_cols):
      """Processes the intercept term.
  
      Merges intercept in beta and dummy column in x if they are not there.
      Appends "(Intercept)" to the front of ``pred_cols`` if it is not there.
  
      Parameters
      ----------
      x : `numpy.array`
          The design matrix.
      beta : `numpy.array`
          The estimated coefficients.
      intercept : `float`
          The estimated intercept.
      pred_cols : `list` [ `str` ]
          The names for predictors.
  
      Returns
      -------
      x : `numpy.array`
          The design matrix with dummy column.
      beta : `numpy.array`
          The estimated coefficients with intercept in the first position.
      pred_cols : `list` [ `str` ]
          List of names of predictors, with "Intercept" in the first position.
      """
      beta = np.copy(beta.ravel())
      x = np.copy(x)
  
      # Checks if x has an intercept column
      if not all(x[:, 0] == 1):
          x = np.concatenate([np.ones([x.shape[0], 1]), x], axis=1)
      # Checks beta has intercept column.
      # In this case, the coefficient for intercept column should be zero.
      # Use intercept as the coefficient for beta column
      if x.shape[1] == beta.shape[0]:
          beta[0] += intercept  # combines the intercept term
      # If beta does not have intercept term, concatenate the intercept term.
      elif x.shape[1] == beta.shape[0] + 1:
          beta = np.concatenate([[intercept], beta])
      else:
          raise ValueError(
              "The shape of x and beta do not match. "
              f"x has shape ({x.shape[0]}, {x.shape[1]}) with the intercept column, "
              f"but beta has length {len(beta)}."
          )
      # Processes pred_cols
      if len(pred_cols) == x.shape[1] - 1:
          pred_cols = [INTERCEPT] + pred_cols
      elif len(pred_cols) == x.shape[1] and "Intercept" in pred_cols[0]:
          pass
      else:
          raise ValueError(
              "The length of pred_cols does not match the shape of x. "
              f"x has shape ({x.shape[0]}, {x.shape[1]}) with the intercept column, "
              f"but pred_cols has length {len(pred_cols)}."
          )
      return x, beta, pred_cols
  
imports: import numpy
  import pandas
  import statsmodels
  import statsmodels.api
  from scipy.stats import f
  from scipy.stats import norm
  from scipy.stats import t
  from sklearn.base import clone
  from sklearn.linear_model import Ridge
  from sklearn.model_selection import train_test_split
  from greykite.algo.common.col_name_utils import INTERCEPT
  from greykite.algo.common.col_name_utils import simplify_pred_cols
label_desc: Use image node_id 1 for calling a global function with example usage: process_intercept(x, beta, intercept, pred_cols) and returns: x,  beta,  pred_cols