code: def gen_sliced_df(
      sample_size_dict={"a": 100, "b": 200, "c": 300, "d": 8, "e": 3},
      seed_dict={
          "a": 301,
          "b": 167,
          "c": 593,
          "d": 893,
          "e": 191,
          "z": 397,
      },
      err_magnitude_coef=1.0,
  ):
      """generates a data frame which includes a response variable with column name "y", and an
      estimate of y with column name "y_hat". y is designed to be a function of a categorical
      variable given in "x" and a continuous variable given in "z".
      For various levels of y, the variance of y is different and the sample size is also different.
      The noises added are all deterministic so that this data set does not change at random
      """
  
      y_a = np.linspace(
          start=90, stop=100, num=sample_size_dict["a"], endpoint=True
      )
      np.random.seed(seed=seed_dict["a"])
      y_a_hat = y_a + err_magnitude_coef * np.random.random(len(y_a))
  
      y_b = np.linspace(
          start=190, stop=200, num=sample_size_dict["b"], endpoint=True
      )
      np.random.seed(seed=seed_dict["b"])
      y_b_hat = y_b + err_magnitude_coef * 1.5 * np.random.random(
          len(y_b)
      )
  
      y_c = np.linspace(
          start=290, stop=300, num=sample_size_dict["c"], endpoint=True
      )
      np.random.seed(seed=seed_dict["c"])
      y_c_hat = y_c + err_magnitude_coef * 2 * np.random.random(
          len(y_c)
      )
  
      y_d = np.linspace(
          start=490, stop=550, num=sample_size_dict["d"], endpoint=True
      )
      np.random.seed(seed=seed_dict["d"])
      y_d_hat = y_d + err_magnitude_coef * np.random.random(len(y_d))
  
      y_e = np.linspace(
          start=-10, stop=0, num=sample_size_dict["e"], endpoint=True
      )
      np.random.seed(seed=seed_dict["e"])
      y_e_hat = y_e + err_magnitude_coef * 3 * np.random.random(
          len(y_e)
      )
  
      y = np.concatenate((y_a, y_b, y_c, y_d, y_e), axis=0, out=None)
      y_hat = np.concatenate(
          (y_a_hat, y_b_hat, y_c_hat, y_d_hat, y_e_hat),
          axis=0,
          out=None,
      )
  
      # also create a continuous covariate which might be useful in some simulations
      np.random.seed(seed=seed_dict["z"])
      z = np.random.random(len(y))
      y = y + 2 * z
      y_hat = y_hat + 2.1 * z
  
      df = pd.DataFrame(
          {
              "x": ["a"] * len(y_a)
              + ["b"] * len(y_b)
              + ["c"] * len(y_c)
              + ["d"] * len(y_d)
              + ["e"] * len(y_e),
              "z": z,
              "y": y,
              "y_hat": y_hat,
          }
      )
      df["residual"] = df["y"] - df["y_hat"]
      # adding another categorical column
      df["z_categ"] = df["z"].round().astype(str)
  
      return df
  
imports: import datetime
  import warnings
  import numpy
  import pandas
  from greykite.common.constants import ADJUSTMENT_DELTA_COL
  from greykite.common.constants import ANOMALY_COL
  from greykite.common.constants import END_TIME_COL
  from greykite.common.constants import EVENT_DF_LABEL_COL
  from greykite.common.constants import METRIC_COL
  from greykite.common.constants import START_TIME_COL
  from greykite.common.constants import TIME_COL
  from greykite.common.constants import VALUE_COL
  from greykite.common.constants import TimeFeaturesEnum
  from greykite.common.features.timeseries_features import add_daily_events
  from greykite.common.features.timeseries_features import build_time_features_df
  from greykite.common.features.timeseries_features import fourier_series_multi_fcn
  from greykite.common.features.timeseries_features import get_default_origin_for_time_vars
  from greykite.common.features.timeseries_features import get_fourier_col_name
  from greykite.common.features.timeseries_features import get_holidays
  from greykite.common.python_utils import assert_equal
label_desc: Use image node_id 9 for calling a global function with example usage: gen_sliced_df(sample_size_dict, seed_dict, err_magnitude_coef) and returns: df