code: def test_predict_bootstrapping_output_when_forecaster_is_LinearRegression_steps_is_2_in_sample_residuals_False_exog_and_transformer():
      """
      Test output of predict_bootstrapping when regressor is LinearRegression,
      2 steps are predicted, using in-sample residuals, exog is included and both
      inputs are transformed.
      """
      forecaster = ForecasterAutoregMultiVariate(
          regressor=LinearRegression(),
          steps=2,
          level="l1",
          lags=3,
          transformer_series=StandardScaler(),
          transformer_exog=transformer_exog,
      )
      forecaster.fit(series=series, exog=exog)
      forecaster.out_sample_residuals = forecaster.in_sample_residuals
      results = forecaster.predict_bootstrapping(
          steps=2,
          exog=exog_predict,
          n_boot=4,
          in_sample_residuals=False,
      )
      expected = pd.DataFrame(
          data=np.array(
              [
                  [0.68370403, 0.61428329, 0.38628787, 0.46804785],
                  [0.53932503, 0.13843292, 0.39752999, 0.86694953],
              ]
          ),
          columns=[f"pred_boot_{i}" for i in range(4)],
          index=pd.RangeIndex(start=50, stop=52),
      )
  
      pd.testing.assert_frame_equal(expected, results)
  
imports: import re
  import pytest
  import numpy
  import pandas
  from sklearn.exceptions import NotFittedError
  from skforecast.ForecasterAutoregMultiVariate import ForecasterAutoregMultiVariate
  from sklearn.linear_model import LinearRegression
  from sklearn.compose import ColumnTransformer
  from sklearn.preprocessing import StandardScaler
  from sklearn.preprocessing import OneHotEncoder
  from .fixtures_ForecasterAutoregMultiVariate import series
  from .fixtures_ForecasterAutoregMultiVariate import exog
  from .fixtures_ForecasterAutoregMultiVariate import exog_predict
label_desc: Use image node_id 8 for calling a global function with example usage: test_predict_bootstrapping_output_when_forecaster_is_LinearRegression_steps_is_2_in_sample_residuals_False_exog_and_transformer() without return types