code: def test_output_backtesting_forecaster_fixed_train_size_no_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, no exog,
      12 observations to backtest, steps=5 (2 remainder), metric='mean_squared_error',
      fixed_train_size=True
      """
      expected_metric = 0.07217085374372428
      expected_predictions = pd.DataFrame(
          {
              "pred": np.array(
                  [
                      0.55717779,
                      0.43355138,
                      0.54969767,
                      0.52945466,
                      0.48308861,
                      0.4909399,
                      0.47942107,
                      0.46025344,
                      0.46649132,
                      0.47061725,
                      0.57603136,
                      0.41480551,
                  ]
              )
          },
          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=None,
          refit=True,
          initial_train_size=len(y_train),
          fixed_train_size=True,
          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 17 for calling a global function with example usage: test_output_backtesting_forecaster_fixed_train_size_no_exog_yes_remainder_with_mocked() without return types