Apprendre Building Polynomial Regression

Loading File

We load poly.csv and inspect it:


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import pandas as pd
file_link = 'https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/poly.csv'
df = pd.read_csv(file_link)
print(df.head())

Then visualize the relation:


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import matplotlib.pyplot as plt
X = df['Feature']
y = df['Target']
plt.scatter(X, y)
plt.show()

A straight line fits poorly, so Polynomial Regression is more suitable.

Building X̃ Matrix

To create X̃, we could add squared features manually:

df['Feature_squared'] = df['Feature'] ** 2

But for higher degrees, PolynomialFeatures is easier. It requires a 2-D structure:

from sklearn.preprocessing import PolynomialFeatures
X = df[['Feature']]
poly = PolynomialFeatures(n)
X_tilde = poly.fit_transform(X)

It also adds the constant column, so no sm.add_constant() needed.

If X is 1-D, convert it:

X = X.reshape(-1, 1)

Building the Polynomial Regression

import statsmodels.api as sm
y = df['Target']
X = df[['Feature']]
X_tilde = PolynomialFeatures(n).fit_transform(X)
model = sm.OLS(y, X_tilde).fit()

Predicting requires transforming new data the same way:

X_new_tilde = PolynomialFeatures(n).fit_transform(X_new)
y_pred = model.predict(X_new_tilde)

Full Example


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import pandas as pd, numpy as np, matplotlib.pyplot as plt
import statsmodels.api as sm
from sklearn.preprocessing import PolynomialFeatures

df = pd.read_csv(file_link)
n = 2
X = df[['Feature']]
y = df['Target']
X_tilde = PolynomialFeatures(n).fit_transform(X)
model = sm.OLS(y, X_tilde).fit()

X_new = np.linspace(-0.1, 1.5, 80).reshape(-1,1)
X_new_tilde = PolynomialFeatures(n).fit_transform(X_new)
y_pred = model.predict(X_new_tilde)

plt.scatter(X, y)
plt.plot(X_new, y_pred)
plt.show()

Try different n values to see how the curve changes and how predictions behave outside the original feature range—this leads into the next chapter.

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Section 1. Chapitre 13

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