code: def test_noformula_prediction(self, close_figures):
      np.random.seed(6434)
      n = 200
      x1 = np.random.normal(size=n)
      x2 = np.random.normal(size=n)
      x3 = np.random.normal(size=n)
      y = x1 - x2 + np.random.normal(size=n)
  
      exog = np.vstack((x1, x2, x3)).T
  
      model = sm.OLS(y, exog)
      result = model.fit()
  
      summaries = {"x3": pctl(0.75)}
      values = {"x2": 1}
      pr1, ci1, fvals1 = predict_functional(
          result, "x1", summaries, values
      )
  
      values = {"x2": -1}
      pr2, ci2, fvals2 = predict_functional(
          result, "x1", summaries, values
      )
  
      plt.clf()
      fig = plt.figure()
      ax = plt.axes([0.1, 0.1, 0.7, 0.8])
      plt.plot(
          fvals1,
          pr1,
          "-",
          label="x2=1",
          lw=4,
          alpha=0.6,
          color="orange",
      )
      plt.plot(
          fvals2, pr2, "-", label="x2=-1", lw=4, alpha=0.6, color="lime"
      )
      ha, lb = ax.get_legend_handles_labels()
      leg = plt.figlegend(ha, lb, loc="center right")
      leg.draw_frame(False)
      plt.xlabel("Focus variable", size=15)
      plt.ylabel("Fitted mean", size=15)
      plt.title("Linear model prediction")
      self.close_or_save(fig)
  
      plt.clf()
      fig = plt.figure()
      ax = plt.axes([0.1, 0.1, 0.7, 0.8])
      plt.plot(
          fvals1,
          pr1,
          "-",
          label="x2=1",
          lw=4,
          alpha=0.6,
          color="orange",
      )
      plt.fill_between(fvals1, ci1[:, 0], ci1[:, 1], color="grey")
      plt.plot(
          fvals1, pr2, "-", label="x2=1", lw=4, alpha=0.6, color="lime"
      )
      plt.fill_between(fvals2, ci2[:, 0], ci2[:, 1], color="grey")
      ha, lb = ax.get_legend_handles_labels()
      plt.figlegend(ha, lb, loc="center right")
      plt.xlabel("Focus variable", size=15)
      plt.ylabel("Fitted mean", size=15)
      plt.title("Linear model prediction")
      self.close_or_save(fig)
  
file_path: statsmodels/statsmodels/sandbox/tests/test_predict_functional.py
imports: from statsmodels.sandbox.predict_functional import predict_functional
  import numpy
  import pandas
  import pytest
  import statsmodels.api
label_desc: Use image node_id 9 for calling the TestPredFunc obj's underlying member method code with example usage: obj.test_noformula_prediction(close_figures) without return types