code: def test_formula_predict_series():
      data = pd.DataFrame(
          {"y": [1, 2, 3], "x": [1, 2, 3]}, index=[5, 3, 1]
      )
      results = ols("y ~ x", data).fit()
  
      result = results.predict(data)
      expected = pd.Series([1.0, 2.0, 3.0], index=[5, 3, 1])
      assert_series_equal(result, expected)
  
      result = results.predict(data.x)
      assert_series_equal(result, expected)
  
      result = results.predict(
          pd.Series([1, 2, 3], index=[1, 2, 3], name="x")
      )
      expected = pd.Series([1.0, 2.0, 3.0], index=[1, 2, 3])
      assert_series_equal(result, expected)
  
      result = results.predict({"x": [1, 2, 3]})
      expected = pd.Series([1.0, 2.0, 3.0], index=[0, 1, 2])
      assert_series_equal(result, expected, check_index_type=False)
  
imports: from statsmodels.compat.pandas import assert_series_equal
  from io import StringIO
  import warnings
  import numpy
  import numpy.testing
  import pandas
  import patsy
  import pytest
  from statsmodels.datasets import cpunish
  from statsmodels.datasets.longley import load, load_pandas
  from statsmodels.formula.api import ols
  from statsmodels.formula.formulatools import make_hypotheses_matrices
  from statsmodels.tools import add_constant
  from statsmodels.tools.testing import assert_equal
label_desc: Use image node_id 4 for calling a global function with example usage: test_formula_predict_series() without return types