code: def test_predict_bootstrapping_output_when_forecaster_is_LinearRegression_and_differentiation_is_1():
      """
      Test output of predict_bootstrapping when regressor is LinearRegression and
      differentiation is 1.
      """
      # Data differentiated
      diferenciator = TimeSeriesDifferentiator(order=1)
      data_diff = diferenciator.fit_transform(data)
      data_diff = pd.Series(data_diff, index=data.index).dropna()
      # Simulated exogenous variable
      rng = np.random.default_rng(9876)
      exog = pd.Series(
          rng.normal(loc=0, scale=1, size=len(data)),
          index=data.index,
          name="exog",
      )
      exog_diff = exog.iloc[1:]
      end_train = "2003-03-01 23:59:00"
      steps = len(data.loc[end_train:])
  
      forecaster_1 = ForecasterAutoreg(
          regressor=LinearRegression(), lags=15
      )
      forecaster_1.fit(
          y=data_diff.loc[:end_train], exog=exog_diff.loc[:end_train]
      )
      boot_predictions_diff = forecaster_1.predict_bootstrapping(
          steps=steps, exog=exog_diff.loc[end_train:], n_boot=10
      )
      last_value_train = data.loc[:end_train].iloc[[-1]]
      boot_predictions_1 = boot_predictions_diff.copy()
      boot_predictions_1.loc[
          last_value_train.index[0]
      ] = last_value_train.values[0]
      boot_predictions_1 = boot_predictions_1.sort_index()
      boot_predictions_1 = boot_predictions_1.cumsum(axis=0).iloc[1:,]
      boot_predictions_1 = boot_predictions_1.asfreq("MS")
      forecaster_2 = ForecasterAutoreg(
          regressor=LinearRegression(), lags=15, differentiation=1
      )
      forecaster_2.fit(
          y=data.loc[:end_train], exog=exog.loc[:end_train]
      )
      boot_predictions_2 = forecaster_2.predict_bootstrapping(
          steps=steps, exog=exog_diff.loc[end_train:], n_boot=10
      )
  
      pd.testing.assert_frame_equal(
          boot_predictions_1, boot_predictions_2
      )
  
imports: import re
  import pytest
  import numpy
  import pandas
  from sklearn.exceptions import NotFittedError
  from skforecast.ForecasterAutoreg import ForecasterAutoreg
  from skforecast.preprocessing import TimeSeriesDifferentiator
  from sklearn.linear_model import LinearRegression
  from sklearn.preprocessing import StandardScaler
  from .fixtures_ForecasterAutoreg import y
  from .fixtures_ForecasterAutoreg import exog
  from .fixtures_ForecasterAutoreg import exog_predict
  from .fixtures_ForecasterAutoreg import data
label_desc: Use image node_id 9 for calling a global function with example usage: test_predict_bootstrapping_output_when_forecaster_is_LinearRegression_and_differentiation_is_1() without return types