Polynomial regression pipeline in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of polynomial regression prediction

Given the following code that fits a polynomial regression model and predicts a value, what is the output?

ML Python

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

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

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

model = LinearRegression()
model.fit(X_poly, y)

pred = model.predict(poly.transform([[6]]))
print(round(pred[0], 2))

A 36.0

B 35.0

C 30.0

D 42.0

💡 Hint

Remember that the model fits y = x^2, so predicting for x=6 should be close to 36.

The model fits a polynomial of degree 2 to the data y = x^2. Predicting for x=6 gives approximately 36.

❓ Model Choice

intermediate

Best model choice for polynomial regression pipeline

You want to build a pipeline that fits a polynomial regression model to data. Which of the following pipeline components is the correct choice to transform the input features before fitting a linear regression?

A MinMaxScaler followed by LinearRegression

B StandardScaler followed by LinearRegression

C PolynomialFeatures followed by LinearRegression

D PCA followed by LinearRegression

💡 Hint

Polynomial regression requires creating polynomial features before fitting a linear model.

PolynomialFeatures generates polynomial terms needed for polynomial regression. The other options do not create polynomial features.

❓ Hyperparameter

advanced

Choosing the polynomial degree hyperparameter

In a polynomial regression pipeline, which effect does increasing the degree hyperparameter have on the model?

A It has no effect on model complexity

B It increases model complexity and may cause overfitting

C It decreases model complexity and reduces overfitting

D It always improves model generalization

💡 Hint

Higher degree polynomials can fit data more closely but risk fitting noise.

Increasing degree adds more polynomial terms, making the model more flexible and prone to overfitting.

❓ Metrics

advanced

Evaluating polynomial regression with R² score

After fitting a polynomial regression model, you compute the R² score on test data and get 0.95. What does this value indicate?

A The model explains 95% of the variance in the test data

B The model has 95% accuracy in classification

C The model's predictions are 95% correct on average

D The model has 95% error rate

💡 Hint

R² score measures how well the model explains variance in continuous data.

R² of 0.95 means the model explains 95% of the variance in the target variable on test data.

🔧 Debug

expert

Debugging pipeline with incorrect feature transformation

You build a pipeline with PolynomialFeatures(degree=3) and LinearRegression. After training, predictions are constant and do not change with input. What is the most likely cause?

A PolynomialFeatures was not fitted before transforming the input

B LinearRegression was not fitted with the transformed features

C Degree parameter was set to 1 instead of 3

D Input data was not reshaped to 2D array before transformation

💡 Hint

PolynomialFeatures expects 2D input; wrong shape can cause incorrect transformations.

If input is 1D array, PolynomialFeatures treats it incorrectly, leading to constant predictions.

Practice

1.

What is the main purpose of using polynomial regression instead of simple linear regression?

easy

A. To fit curved relationships between variables

B. To reduce the number of features

C. To speed up training time

D. To handle missing data automatically

Solution

1. Step 1: Understand linear regression limitation

   Linear regression fits straight lines, which cannot capture curves in data.

2. Step 2: Role of polynomial regression

   Polynomial regression fits curved lines by adding powers of features, capturing non-linear patterns.

3. Final Answer:

   To fit curved relationships between variables -> Option A

4. Quick Check:

   Polynomial regression = curved fit [OK]

Hint: Polynomial regression fits curves, not just straight lines [OK]

Common Mistakes:

• Thinking polynomial regression reduces features
• Assuming it speeds up training
• Believing it handles missing data automatically

2.

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())
])

easy

A. pipeline = Pipeline([('poly', PolynomialFeatures(degree=2)), ('linear', LinearRegression())])

B. pipeline = Pipeline([('linear', LinearRegression()), ('poly', PolynomialFeatures(degree=2))])

C. pipeline = Pipeline([('poly', LinearRegression()), ('linear', PolynomialFeatures(degree=2))])

D. pipeline = Pipeline([('poly', PolynomialFeatures()), ('linear', LinearRegression(degree=2))])

Solution

1. Step 1: Order of pipeline steps

   PolynomialFeatures must come before LinearRegression to transform data first.

2. Step 2: Correct usage of classes and parameters

   PolynomialFeatures takes degree parameter; LinearRegression does not take degree.

3. Final Answer:

   pipeline = Pipeline([('poly', PolynomialFeatures(degree=2)), ('linear', LinearRegression())]) -> Option A

4. Quick Check:

   PolynomialFeatures before LinearRegression [OK]

Hint: Put PolynomialFeatures before LinearRegression in pipeline [OK]

Common Mistakes:

• Swapping order of pipeline steps
• Passing degree to LinearRegression
• Omitting degree in PolynomialFeatures

3.

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))

medium

A. [10.0]

B. [8.0]

C. [4.0]

D. [16.0]

Solution

1. Step 1: Understand data and model

   X = [[1],[2],[3]] with y = [1,4,9] fits y = x^2 perfectly.

2. Step 2: Predict for X=4 using polynomial degree 2

   Model learns y = x^2, so prediction at 4 is 4^2 = 16.

3. Final Answer:

   [16.0] -> Option D

4. Quick Check:

   4 squared = 16 [OK]

Hint: Polynomial degree 2 fits squares; predict 4^2 = 16 [OK]

Common Mistakes:

• Ignoring polynomial transformation
• Predicting linear value instead of squared
• Rounding errors without np.round

4.

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)

medium

A. LinearRegression should not be used in pipeline

B. The order of pipeline steps is incorrect

C. PolynomialFeatures degree must be 2, not 3

D. Missing import for X_train and y_train

Solution

1. Step 1: Check pipeline step order

   PolynomialFeatures must come before LinearRegression to transform data first.

2. Step 2: Confirm degree and imports

   Degree 3 is valid; imports for data are assumed outside snippet.

3. Final Answer:

   The order of pipeline steps is incorrect -> Option B

4. Quick Check:

   PolynomialFeatures before LinearRegression [OK]

Hint: PolynomialFeatures must be first in pipeline [OK]

Common Mistakes:

• Swapping order of steps
• Thinking degree must be 2
• Confusing missing data imports with pipeline error

5.

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?

hard

A. Remove polynomial features and use linear regression only

B. Decrease the polynomial degree to avoid overfitting

C. Increase the polynomial degree to capture more complexity

D. Use degree=2 but reduce training data size

Solution

1. Step 1: Understand model complexity and fit

   Degree 2 polynomial may be too simple for complex curves, causing poor fit.

2. Step 2: Adjust polynomial degree

   Increasing degree allows model to fit more complex patterns, improving fit quality.

3. Final Answer:

   Increase the polynomial degree to capture more complexity -> Option C

4. Quick Check:

   Higher degree = better complex fit [OK]

Hint: Raise degree to fit complex curves better [OK]

Common Mistakes:

• Lowering degree when fit is poor
• Removing polynomial features unnecessarily
• Reducing data size instead of model complexity