Lernen Building Polynomial Regression

Loading File

We load poly.csv and inspect it:


              1234
            
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:


              12345
            
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


              123456789101112131415161718
            
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.

War alles klar?

Danke für Ihr Feedback!

Abschnitt 1. Kapitel 13

Fragen Sie AI

Fragen Sie alles oder probieren Sie eine der vorgeschlagenen Fragen, um unser Gespräch zu beginnen

Swipe um das Menü anzuzeigen