Polynomial regression in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the class used for polynomial features.

ML Python

from sklearn.preprocessing import [1]

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ALinearRegression

BStandardScaler

Ctrain_test_split

DPolynomialFeatures

Attempts:

3 left

💡 Hint

Common Mistakes

Importing LinearRegression instead of PolynomialFeatures

Importing unrelated classes like StandardScaler

The PolynomialFeatures class is used to generate polynomial and interaction features from the original features.

2fill in blank

medium

Complete the code to create polynomial features of degree 3.

ML Python

poly = PolynomialFeatures(degree=[1])

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A3

B1

C2

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Using degree 1 which is just linear

Using degree 2 which is quadratic

Setting degree=3 creates polynomial features up to cubic terms.

3fill in blank

hard

Fix the error in transforming features to polynomial features.

ML Python

X_poly = poly.[1](X)

Drag options to blanks, or click blank then click option'

Atransform

Bfit_transform

Cfit

Dpredict

Attempts:

3 left

💡 Hint

Common Mistakes

Using only fit which does not transform data

Using transform without fitting first

fit_transform fits the transformer and applies the transformation in one step, which is needed here.

4fill in blank

hard

Fill both blanks to train a linear regression model on polynomial features.

ML Python

model = LinearRegression()
model.[1](X_poly, y)
predictions = model.[2](X_poly)

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Afit

Bpredict

Ctransform

Dscore

Attempts:

3 left

💡 Hint

Common Mistakes

Using predict before fit

Using transform or score instead of fit or predict

First, fit trains the model on data. Then, predict generates predictions from the trained model.

5fill in blank

hard

Fill all three blanks to create polynomial features, train the model, and compute the R² score.

ML Python

poly = PolynomialFeatures(degree=[1])
X_poly = poly.[2](X)
model = LinearRegression()
model.fit(X_poly, y)
score = model.[3](X_poly, y)

Drag options to blanks, or click blank then click option'

A3

Bfit_transform

Cscore

Dtransform

Attempts:

3 left

💡 Hint

Common Mistakes

Using transform instead of fit_transform

Using predict instead of score for evaluation

Degree 3 creates cubic features. fit_transform prepares the features. score computes the R² metric to evaluate the model.

Practice

1. What is the main purpose of polynomial regression in machine learning?

easy

A. To perform clustering on unlabeled data

B. To reduce the number of features in the dataset

C. To classify data into categories

D. To model non-linear relationships by adding powers of input features

Solution

1. Step 1: Understand the goal of polynomial regression

   Polynomial regression extends linear regression by adding powers of input features to capture curves in data.

2. Step 2: Compare options with this goal

   Only To model non-linear relationships by adding powers of input features describes modeling non-linear relationships by adding powers of features, which matches polynomial regression.

3. Final Answer:

   To model non-linear relationships by adding powers of input features -> Option D

4. Quick Check:

   Polynomial regression = model curves [OK]

Hint: Polynomial regression fits curves by adding powers of inputs [OK]

Common Mistakes:

• Confusing polynomial regression with classification
• Thinking it reduces features instead of expanding them
• Mixing it up with clustering methods

2. Which Python code snippet correctly creates polynomial features of degree 3 using scikit-learn?

easy

A. from sklearn.linear_model import PolynomialFeatures
poly = PolynomialFeatures(3)
X_poly = poly.transform(X)

B. from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=3)
X_poly = poly.fit_transform(X)

C. from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=2)
X_poly = poly.fit(X)

D. from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=3)
X_poly = poly.transform(X)

Solution

1. Step 1: Check import and class usage

   PolynomialFeatures is in sklearn.preprocessing, so import must be from there.

2. Step 2: Verify method calls and degree

   Degree=3 is correct. fit_transform(X) creates polynomial features properly. from sklearn.preprocessing import PolynomialFeatures poly = PolynomialFeatures(degree=3) X_poly = poly.fit_transform(X) matches all these.

3. Final Answer:

   from sklearn.preprocessing import PolynomialFeatures poly = PolynomialFeatures(degree=3) X_poly = poly.fit_transform(X) -> Option B

4. Quick Check:

   Correct import + degree + fit_transform = A [OK]

Hint: Use fit_transform with PolynomialFeatures from sklearn.preprocessing [OK]

Common Mistakes:

• Importing PolynomialFeatures from wrong module
• Using transform without fit first
• Setting wrong degree value

3. Given this code, what will be the shape of X_poly if X has shape (5, 1) and degree=2?

from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=2)
X_poly = poly.fit_transform(X)

medium

A. (5, 1)

B. (5, 2)

C. (5, 3)

D. (5, 4)

Solution

1. Step 1: Understand PolynomialFeatures output shape

   For degree=2 and one feature, output includes [1, x, x^2], so 3 features total.

2. Step 2: Calculate shape based on input rows and new features

   Input has 5 rows, so output shape is (5, 3).

3. Final Answer:

   (5, 3) -> Option C

4. Quick Check:

   Degree 2 with 1 feature = 3 columns [OK]

Hint: Output columns = combinations with degree + 1 for bias [OK]

Common Mistakes:

• Forgetting the bias (constant 1) column
• Assuming output shape equals input shape
• Confusing degree with number of features

4. Identify the error in this polynomial regression code snippet:

from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
poly = PolynomialFeatures(degree=2)
X_poly = poly.transform(X)
model = LinearRegression()
model.fit(X_poly, y)

medium

A. Using transform before fitting PolynomialFeatures

B. LinearRegression cannot be used with polynomial features

C. Missing import for LinearRegression

D. Degree should be 1 for polynomial regression

Solution

1. Step 1: Check usage of PolynomialFeatures methods

   PolynomialFeatures must be fitted before transform; fit_transform fits and transforms in one step.

2. Step 2: Identify the error in code

   Code calls poly.transform(X) without fitting first, causing error. Correct is poly.fit_transform(X).

3. Final Answer:

   Using transform before fitting PolynomialFeatures -> Option A

4. Quick Check:

   fit_transform needed before transform [OK]

Hint: Always fit PolynomialFeatures before transform or use fit_transform [OK]

Common Mistakes:

• Calling transform without fit first
• Thinking LinearRegression can't handle polynomial features
• Ignoring method order in preprocessing

5. You have data with a clear curve pattern. You fit a polynomial regression model with degree 5 and get very low training error but high error on new data. What is the best next step?

hard

A. Reduce the polynomial degree to avoid overfitting

B. Increase the polynomial degree to 10 for better fit

C. Remove polynomial features and use linear regression only

D. Add more polynomial features of degree 6

Solution

1. Step 1: Understand the problem of low training but high test error

   This indicates overfitting: model fits training data too closely but fails to generalize.

2. Step 2: Choose a solution to reduce overfitting

   Reducing polynomial degree simplifies the model, helping it generalize better on new data.

3. Final Answer:

   Reduce the polynomial degree to avoid overfitting -> Option A

4. Quick Check:

   Overfitting? Lower degree polynomial [OK]

Hint: Lower degree to reduce overfitting when test error is high [OK]

Common Mistakes:

• Increasing degree worsens overfitting
• Removing polynomial features loses curve fit
• Adding higher degree features increases complexity