code: def test_predict_bootstrapping_output_when_forecaster_is_LinearRegression_exog_steps_is_2_in_sample_residuals_is_False():
      """
      Test output of predict_bootstrapping when regressor is LinearRegression and
      2 steps ahead are predicted with exog using out-sample residuals.
      """
      forecaster = ForecasterAutoregMultiSeriesCustom(
          regressor=LinearRegression(),
          fun_predictors=create_predictors,
          window_size=3,
          transformer_series=None,
      )
      forecaster.fit(series=series, exog=exog["exog_1"])
      forecaster.out_sample_residuals = forecaster.in_sample_residuals
      results = forecaster.predict_bootstrapping(
          steps=2,
          n_boot=4,
          exog=exog_predict["exog_1"],
          in_sample_residuals=False,
      )
  
      expected_1 = pd.DataFrame(
          data=np.array(
              [
                  [0.16386591, 0.56398143, 0.38576231, 0.37782729],
                  [0.04906615, 0.45019329, 0.07478854, 0.222437],
              ]
          ),
          columns=[f"pred_boot_{i}" for i in range(4)],
          index=pd.RangeIndex(start=50, stop=52),
      )
      expected_2 = pd.DataFrame(
          data=np.array(
              [
                  [0.24898667, 0.69862572, 0.72572763, 0.45672811],
                  [0.29374176, 0.40758093, 0.74577937, 0.11883889],
              ]
          ),
          columns=[f"pred_boot_{i}" for i in range(4)],
          index=pd.RangeIndex(start=50, stop=52),
      )
  
      expected = {"1": expected_1, "2": expected_2}
  
      for key in results.keys():
          pd.testing.assert_frame_equal(results[key], expected[key])
  
imports: import re
  import pytest
  import numpy
  import pandas
  from sklearn.exceptions import NotFittedError
  from skforecast.ForecasterAutoregMultiSeriesCustom import ForecasterAutoregMultiSeriesCustom
  from sklearn.compose import ColumnTransformer
  from sklearn.preprocessing import StandardScaler
  from sklearn.preprocessing import OneHotEncoder
  from sklearn.linear_model import LinearRegression
  from .fixtures_ForecasterAutoregMultiSeriesCustom import series
  from .fixtures_ForecasterAutoregMultiSeriesCustom import exog
  from .fixtures_ForecasterAutoregMultiSeriesCustom import exog_predict
label_desc: Use image node_id 11 for calling a global function with example usage: test_predict_bootstrapping_output_when_forecaster_is_LinearRegression_exog_steps_is_2_in_sample_residuals_is_False() without return types