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Polynomial regression helps us find curved lines that fit data better than straight lines. A pipeline makes it easy to do all steps together without mistakes.
from sklearn.pipeline import Pipeline from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression pipeline = Pipeline([ ('poly_features', PolynomialFeatures(degree=2)), ('linear_regression', LinearRegression()) ]) pipeline.fit(X_train, y_train) predictions = pipeline.predict(X_test)
The pipeline runs steps in order: first it creates polynomial features, then fits a linear model.
Change degree to control curve complexity (2 means square terms).
pipeline = Pipeline([
('poly_features', PolynomialFeatures(degree=3)),
('linear_regression', LinearRegression())
])pipeline = Pipeline([
('poly_features', PolynomialFeatures(degree=1)),
('linear_regression', LinearRegression())
])This program creates curved data, fits a polynomial regression model using a pipeline, and shows how well it predicts new points.
import numpy as np from sklearn.pipeline import Pipeline from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression from sklearn.metrics import mean_squared_error # Create sample data: y = 1 + 2x + 3x^2 + noise np.random.seed(0) X = np.linspace(-3, 3, 100).reshape(-1, 1) y = 1 + 2 * X.flatten() + 3 * X.flatten()**2 + np.random.randn(100) * 3 # Split data into train and test X_train, X_test = X[:80], X[80:] y_train, y_test = y[:80], y[80:] # Build polynomial regression pipeline with degree 2 pipeline = Pipeline([ ('poly_features', PolynomialFeatures(degree=2)), ('linear_regression', LinearRegression()) ]) # Train model pipeline.fit(X_train, y_train) # Predict on test data predictions = pipeline.predict(X_test) # Calculate mean squared error mse = mean_squared_error(y_test, predictions) # Print results print(f"Mean Squared Error: {mse:.2f}") print(f"Predictions: {predictions[:5]}")
PolynomialFeatures adds new columns like x², x³ to help model curves.
Using a pipeline avoids mistakes by running all steps together.
Higher degree means more complex curves but can cause overfitting.
Polynomial regression fits curved lines to data.
Pipelines combine data changes and model training in one step.
Adjust degree to control curve complexity and fit quality.
What is the main purpose of using polynomial regression instead of simple linear regression?
Which of the following is the correct way to create a polynomial regression pipeline in Python using sklearn?
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
pipeline = Pipeline([
('poly', PolynomialFeatures(degree=2)),
('linear', LinearRegression())
])Given the following code, what will print(y_pred) output?
import numpy as np
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
X = np.array([[1], [2], [3]])
y = np.array([1, 4, 9])
pipeline = Pipeline([
('poly', PolynomialFeatures(degree=2)),
('linear', LinearRegression())
])
pipeline.fit(X, y)
y_pred = pipeline.predict(np.array([[4]]))
print(np.round(y_pred, 2))Identify the error in this polynomial regression pipeline code:
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
pipeline = Pipeline([
('linear', LinearRegression()),
('poly', PolynomialFeatures(degree=3))
])
pipeline.fit(X_train, y_train)You want to model a dataset with a complex curve. You try polynomial regression with degree=2 but the fit is poor. What is the best next step?