Polynomial regression in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Polynomial Regression Degree

Which statement best describes the role of the degree in polynomial regression?

A The degree controls the highest power of the input features, allowing the model to fit more complex curves.

B The degree determines the number of input features used in the model.

C The degree sets the number of output variables the model predicts.

D The degree limits the number of training samples used during fitting.

❓ Predict Output

intermediate

Output of Polynomial Feature Transformation

What is the output of the following code snippet?

ML Python

from sklearn.preprocessing import PolynomialFeatures
import numpy as np
X = np.array([[2]])
poly = PolynomialFeatures(degree=3, include_bias=False)
result = poly.fit_transform(X)
print(result)

A [[2. 4. 8.]]

B [[2. 4.]]

C [[2. 3. 4.]]

D [[1. 2. 4. 8.]]

❓ Hyperparameter

advanced

Choosing Degree to Avoid Overfitting

You have a dataset with noisy data points. Which degree choice for polynomial regression is most likely to avoid overfitting?

A Degree 10, because higher degree fits data perfectly.

B Degree 1, because it fits a simple straight line.

C Degree 5, as a moderate complexity balance.

D Degree 0, which fits a constant value.

❓ Metrics

advanced

Interpreting Polynomial Regression Metrics

After training a polynomial regression model, you get these metrics on test data: Mean Squared Error (MSE) = 0.02, R² = 0.95. What does this tell you?

A The model has high error and poor fit to the data.

B The model fits the data well with low error and explains 95% of variance.

C The model is underfitting because MSE is too low.

D The model explains only 2% of the variance.

🔧 Debug

expert

Debugging Polynomial Regression Prediction Error

Consider this code snippet for polynomial regression prediction. What is the main reason the predictions are all zeros?

ML Python

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

X_train = np.array([[1], [2], [3], [4]])
y_train = np.array([1, 4, 9, 16])

poly = PolynomialFeatures(degree=2)
X_poly = poly.fit_transform(X_train)

model = LinearRegression()
model.fit(X_train, y_train)

X_test = np.array([[5], [6]])
X_test_poly = poly.transform(X_test)
predictions = model.predict(X_test_poly)
print(predictions)

A The training labels y_train are incorrect for polynomial regression.

B The degree of PolynomialFeatures is too low to capture the data pattern.

C The test data X_test is not transformed before prediction.

D The model was trained on original features, but predictions use polynomial features, causing mismatch.