I’m new to regression analysis in python and greatly appreciate your help:

I have a formula (Y = x1 + Ax1^2 + Bx2^2 + Cx3^2 + Constant), and a dataset to train the model. The dataset includes a column for each Y, x1, x2, x3, and the Month. See example dataset here

I’d like the regression analysis to run 12 times, once for each Month – such that I’ll be able to see a table of 12 rows (one for each month) with coefficients and constants to reference for calculating predictions.

Presently I have the following code set up which does not present the modelrun coefficients and intercepts by month. Can someone help me add to the code to present a table of coefficients and constants, one row for each month?

import numpy as np
import pandas as pd
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression

#Read dataset
df = pd.read_csv('StackOverdlow - Example Dataset 20240621.csv')

#Replace negative y with zero
df.y[df.y<0]=0


def _reg(df):
    df['y'] = df['y'].apply(lambda x: max(0, x))
    res = pd.DataFrame(columns=['Month', 'Intercept', 'x1', 'x1^2', 'x2', 'x2^2', 'x3', 'x3^2'])

    for month in range(1, 12 + 1):
        MD = df[df['Month'] == month]
        X = MD[['x1', 'x2', 'x3']].values
        y = MD['y'].values

        poly = PolynomialFeatures(degree=2, include_bias=False)
        X_poly = poly.fit_transform(X)

        model = LinearRegression()
        model.fit(X_poly, y)

        C, I = model.coef_, model.intercept_

        row = {
            'Month': month,
            'Intercept': I,
            'x1': C[0],
            'x1^2': C[1],
            'x2': C[2],
            'x2^2': C[3],
            'x3': C[4],
            'x3^2': C[5]
        }

        res = res._append(row, ignore_index=True)

    return res

I tried the above code with the following recommended code appended and it does not pull the actual coefficients from the model run.

D = {
    'Month': np.tile(np.arange(1, 12 + 1), 10),
    'x1': np.random.rand(120),
    'x2': np.random.rand(120),
    'x3': np.random.rand(120),
    'y': np.random.rand(120) * 100
}

print(_reg(pd.DataFrame(D)))