code: def test_output_backtesting_forecaster_yes_exog_yes_remainder_with_mocked():
      """
      Test output of _backtesting_forecaster with backtesting mocked, interval no.
      Regressor is LinearRegression with lags=3, Series y is mocked, exog is mocked,
      12 observations to backtest, steps=5 (2 remainder), metric='mean_squared_error'
      """
      expected_metric = 0.061723961096013524
      expected_predictions = pd.DataFrame(
          {
              "pred": np.array(
                  [
                      0.59059622,
                      0.47257504,
                      0.53024098,
                      0.46163343,
                      0.50035119,
                      0.43595809,
                      0.4349167,
                      0.42381237,
                      0.55165332,
                      0.53442833,
                      0.65361802,
                      0.51297419,
                  ]
              )
          },
          index=pd.RangeIndex(start=38, stop=50, step=1),
      )
      forecaster = ForecasterAutoreg(
          regressor=LinearRegression(), lags=3
      )
  
      n_backtest = 12
      y_train = y[:-n_backtest]
  
      metric, backtest_predictions = _backtesting_forecaster(
          forecaster=forecaster,
          y=y,
          exog=exog,
          refit=True,
          initial_train_size=len(y_train),
          fixed_train_size=False,
          steps=5,
          metric="mean_squared_error",
          interval=None,
          n_boot=500,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      assert expected_metric == approx(metric)
      pd.testing.assert_frame_equal(
          expected_predictions, backtest_predictions
      )
  
imports: import pytest
  import numpy
  import pandas
  from pytest import approx
  from sklearn.linear_model import LinearRegression
  from sklearn.linear_model import Ridge
  from sklearn.metrics import mean_squared_error
  from skforecast.ForecasterAutoreg import ForecasterAutoreg
  from skforecast.ForecasterAutoregCustom import ForecasterAutoregCustom
  from skforecast.ForecasterAutoregDirect import ForecasterAutoregDirect
  from skforecast.model_selection.model_selection import _backtesting_forecaster
  from .fixtures_model_selection import y
  from .fixtures_model_selection import exog
  from .fixtures_model_selection import out_sample_residuals
label_desc: Use image node_id 7 for calling a global function with example usage: test_output_backtesting_forecaster_yes_exog_yes_remainder_with_mocked() without return types