Why advanced regression handles non-linearity in ML Python - Challenge Your Understanding

Challenge - 5 Problems

🧠 Conceptual

intermediate

Why can polynomial regression model non-linear data?

Polynomial regression can fit curves instead of straight lines. Why does this help with non-linear data?

A Because it adds powers of input features, allowing the model to capture curves.

B Because it removes noise from data, making it linear.

C Because it uses only linear combinations of features without transformation.

D Because it reduces the number of features to avoid overfitting.

💡 Hint

Think about how adding squared or cubic terms changes the shape of the prediction.

Polynomial regression adds powers of input features (like squared or cubic terms). This lets the model fit curved lines, which helps capture non-linear relationships in data.

❓ Model Choice

intermediate

Which regression model best handles complex non-linear patterns?

You have data with complex curves and interactions. Which regression model is best to capture these patterns?

A Linear regression

B Polynomial regression with degree 3

C Simple mean prediction

D Decision tree regression

💡 Hint

Think about models that split data into regions and fit different values in each.

Decision tree regression splits data into regions and fits simple models in each. This allows it to capture complex non-linear patterns better than polynomial regression of fixed degree.

❓ Predict Output

advanced

Output of polynomial regression prediction

What is the predicted value from this polynomial regression model?

ML Python

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

X = np.array([[2]])
poly = PolynomialFeatures(degree=2, include_bias=False)
X_poly = poly.fit_transform(X)
model = LinearRegression()
model.coef_ = np.array([3, 4])
model.intercept_ = 5
prediction = model.predict(X_poly)
print(prediction[0])

A 19.0

B 17.0

C 27.0

D 23.0

💡 Hint

Calculate 3*x + 4*x^2 + 5 for x=2.

The polynomial features for x=2 are [2, 4]. The prediction is 5 + 3*2 + 4*4 = 5 + 6 + 16 = 27.0.

❓ Metrics

advanced

Which metric best shows improvement in non-linear regression?

You compare linear regression and polynomial regression on the same dataset. Which metric best shows that polynomial regression fits non-linear data better?

A Higher Mean Squared Error (MSE)

B Lower Mean Squared Error (MSE)

C Higher training loss

D Lower number of features

💡 Hint

Think about what a good fit means for error values.

A lower Mean Squared Error means the model predictions are closer to actual values, showing better fit. Polynomial regression usually lowers MSE on non-linear data compared to linear regression.

🔧 Debug

expert

Why does this kernel ridge regression code fail to capture non-linearity?

Given this code snippet, why does the kernel ridge regression model fail to capture non-linear patterns?

ML Python

from sklearn.kernel_ridge import KernelRidge
import numpy as np

X = np.array([[1], [2], [3], [4], [5]])
y = np.array([1, 4, 9, 16, 25])  # y = x^2

model = KernelRidge(alpha=1.0, kernel='linear')
model.fit(X, y)
pred = model.predict(np.array([[6]]))
print(round(pred[0], 2))

A Because the kernel is linear, it cannot model the quadratic relationship.

B Because alpha is too high, causing overfitting.

C Because the input X is not scaled.

D Because the model is missing the intercept term.

💡 Hint

Think about what the kernel function does in kernel ridge regression.

The linear kernel treats the problem like linear regression, so it cannot capture the quadratic pattern y = x^2. Using a non-linear kernel like 'rbf' would help model non-linearity.