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.

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.

For an initial test (without monthly granularity), I attempted to run the following code: I was surprised when I reviewed the model.coef_ that the output was an array with 10 numbers in it, which seemed strange to me as I only defined three x variables.

    import numpy as np
    import matplotlib.pyplot as plt
    import pandas as pd
    from sklearn.model_selection import train_test_split
    from sklearn.preprocessing import PolynomialFeatures
    from sklearn.linear_model import LinearRegression
    from sklearn.metrics import r2_score

    #Read dataset
    dataset = pd.read_csv('dataset.csv')

    #Replace negative y with zero
    dataset.x1[dataset.y<0]=0

    #define x and y
    X = dataset[['x1', 'x2', 'x3']].values
    y = dataset['y'].values

    # Polynomial Features
    poly = PolynomialFeatures(degree=2)
    X_poly = poly.fit_transform(X)

    # Linear Regression model
    model = LinearRegression()
    model.fit(X_poly, y)