curvilinear_example.py

# cd.display.markdown("## Polynomial Regression")
# y = transformed_shifts['deletedEmployeeCount']
# x = transformed_shifts['deletedEmployeeCount']
# model = np.poly1d(np.polyfit(x, y, 20))
# line = np.linspace(
#     transformed_shifts['deletedEmployeeCount'].min(),
#     transformed_shifts['deletedEmployeeCount'].max(),
#     200
# )
# plt.scatter(x, y, color='grey')
# plt.plot(line, model(line))
# # plt.show()
# cd.display.pyplot()
#

import numpy as np
import pandas as pd
import plotly.graph_objects as go
import statsmodels.formula.api as sm


def predict_using_ols_result_coefficients(x: pd.Series) -> pd.Series:
    """Returns the y predicted for equation y = a + b1x + b2*x"""
    # result = (13.6890 + -0.1334*x + 0.0006*x + 0.4685*x)
    result = (1.1294 + -0.6105*x + 0.0714*x)
    return result


def gen_curvilinear_x_and_y():
    """"""
    rng = np.random.RandomState(1)
    raw_x = 8 * rng.rand(50)
    y = np.sin(raw_x) + 0.1 * rng.randn(50)

    inds = raw_x.ravel().argsort()  # Sort x values and get index
    raw_x = raw_x.ravel()[inds]
    y = y[inds]  # Sort y according to x sorted index
    return raw_x, y


x, y = gen_curvilinear_x_and_y()
df = pd.DataFrame({'x': x, 'y': y})
ols_model = sm.ols(
    formula=f'y ~ x + np.power(x, 3)',
    data=df
).fit()
print(ols_model.params)
print(ols_model.summary())

fig = go.Figure()
fig.add_trace(
    go.Scatter(x=x, y=y, mode='markers')
)
line = np.linspace(
    df['x'].values[0],
    df['x'].values[-1],
    200
)
fake_df = pd.DataFrame()
fake_df['x'] = line
fig.add_trace(
    go.Scatter(x=line, y=ols_model.predict(fake_df), mode='lines')
)
fig.show()

import plotly.graph_objects as go
model = np.poly1d(np.polyfit(x, y, 3))
line = np.linspace(
    df['x'].values[0],
    df['x'].values[-1],
    50
)
# plt.scatter(x, y, color='grey')
# plt.plot(line, model(line))
# plt.show()

fig = go.Figure()
fig.add_trace(go.Scatter(x=x, y=y, mode='markers', name='Data', marker={'color': 'grey'}, showlegend=True))
y_fit = model(line)
fig.add_trace(go.Scatter(x=line, y=y_fit, mode='lines', name='Fit', marker={'color': 'blue'}))
fig.update_layout({
    'xaxis': {'showgrid': False, 'title': 'x'},
    'yaxis': {'showgrid': False, 'title': 'y'},
    'paper_bgcolor': 'white',
    'plot_bgcolor': 'white'
})
# fig.show()