code: def test_check_pandas_dataframe_fit_backward():
      for floating in [True, False]:
          iris = load_iris()
          X = iris.data
          y = iris.target
          lr = SoftmaxRegression(random_seed=1)
          sfs1 = SFS(
              lr,
              k_features=2,
              forward=False,
              floating=floating,
              scoring="accuracy",
              cv=0,
              verbose=0,
              n_jobs=1,
          )
  
          df = pd.DataFrame(
              X,
              columns=[
                  "sepal len",
                  "sepal width",
                  "petal len",
                  "petal width",
              ],
          )
  
          sfs1 = sfs1.fit(X, y)
          assert sfs1.k_feature_idx_ == (1, 2)
          assert sfs1.k_feature_names_ == ("1", "2")
          assert sfs1.subsets_[2]["feature_names"] == ("1", "2")
  
          sfs1 = sfs1.fit(df, y)
          assert sfs1.subsets_[3]["feature_names"] == (
              "sepal len",
              "sepal width",
              "petal len",
          )
          assert sfs1.subsets_[2]["feature_names"] == (
              "sepal width",
              "petal len",
          )
          assert sfs1.subsets_[3]["feature_idx"] == (0, 1, 2)
          assert sfs1.subsets_[2]["feature_idx"] == (1, 2)
          assert sfs1.k_feature_idx_ == (1, 2)
          assert sfs1.k_feature_names_ == ("sepal width", "petal len")
  
          sfs1._TESTING_INTERRUPT_MODE = True
          out = sfs1.fit(df, y)
          assert len(out.subsets_.keys()) > 0
          assert sfs1.interrupted_
          assert sfs1.subsets_[3]["feature_names"] == (
              "sepal len",
              "sepal width",
              "petal len",
          )
          assert sfs1.k_feature_idx_ == (0, 1, 2)
          assert sfs1.k_feature_names_ == (
              "sepal len",
              "sepal width",
              "petal len",
          )
  
imports: import numpy
  import pandas
  from numpy import nan
  from numpy.testing import assert_almost_equal
  from packaging.version import Version
  from sklearn import __version__
  from sklearn.datasets import load_iris
  from sklearn.decomposition import PCA
  from sklearn.ensemble import RandomForestClassifier
  from sklearn.linear_model import LinearRegression
  from sklearn.metrics import accuracy_score, make_scorer, roc_auc_score
  from sklearn.model_selection import GridSearchCV, GroupKFold
  from sklearn.neighbors import KNeighborsClassifier
  from sklearn.pipeline import Pipeline
  from mlxtend.classifier import SoftmaxRegression
  from mlxtend.data import boston_housing_data
  from mlxtend.feature_selection import SequentialFeatureSelector
  from mlxtend.utils import assert_raises
label_desc: Use image node_id 40 for calling a global function with example usage: test_check_pandas_dataframe_fit_backward() without return types