Polynomial features in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

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

ML Python

from sklearn.preprocessing import [1]

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

AStandardScaler

BMinMaxScaler

CLinearRegression

DPolynomialFeatures

Attempts:

3 left

💡 Hint

Common Mistakes

Importing a scaler class instead of PolynomialFeatures.

Confusing PolynomialFeatures with regression models.

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])

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

A3

B1

C2

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Using degree 1 which does not add polynomial features.

Choosing degree 2 when cubic features are needed.

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

3fill in blank

hard

Fix the error in the code to transform features using polynomial features.

ML Python

X_poly = poly.[1](X)

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

Apredict

Btransform

Cfit_transform

Dfit

Attempts:

3 left

💡 Hint

Common Mistakes

Using only fit which does not transform data.

Using transform without fitting first.

The fit_transform method fits the transformer and applies the transformation in one step.

4fill in blank

hard

Fill both blanks to create polynomial features and exclude the bias term.

ML Python

poly = PolynomialFeatures(degree=[1], include_bias=[2])

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

A3

BTrue

CFalse

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Forgetting to exclude the bias term when not needed.

Using the wrong degree for the polynomial features.

Degree 3 creates cubic features. Setting include_bias=False excludes the constant term.

5fill in blank

hard

Fill all three blanks to create polynomial features, transform data, and print the shape of the result.

ML Python

poly = PolynomialFeatures(degree=[1], include_bias=[2])
X_poly = poly.[3](X)

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

A2

BFalse

Cfit_transform

DTrue

Attempts:

3 left

💡 Hint

Common Mistakes

Including bias when not needed.

Using transform without fitting first.

Degree 2 creates quadratic features. Bias is excluded with False. fit_transform fits and transforms the data.

Practice

1. What is the main purpose of using PolynomialFeatures in machine learning?

easy

A. To create new features by adding powers and combinations of existing features

B. To reduce the number of features in the dataset

C. To normalize the data between 0 and 1

D. To split the dataset into training and testing sets

Solution

1. Step 1: Understand the role of PolynomialFeatures

   PolynomialFeatures generates new features by raising existing features to powers and combining them, helping models learn curves.

2. Step 2: Compare with other options

   Feature reduction, normalization between 0 and 1, and splitting into training/testing sets describe different preprocessing steps, not feature creation with powers.

3. Final Answer:

   To create new features by adding powers and combinations of existing features -> Option A

4. Quick Check:

   PolynomialFeatures = create new polynomial features [OK]

Hint: PolynomialFeatures adds powers and combos of features [OK]

Common Mistakes:

• Confusing feature creation with normalization
• Thinking it reduces features instead of expanding
• Mixing it up with data splitting

2. Which of the following is the correct way to import and create polynomial features of degree 2 using scikit-learn?

easy

A. from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=2)

B. from sklearn.linear_model import PolynomialFeatures
poly = PolynomialFeatures(2)

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

D. from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(3)

Solution

1. Step 1: Check the correct import statement

   PolynomialFeatures is in sklearn.preprocessing, so 'from sklearn.preprocessing import PolynomialFeatures' is correct.

2. Step 2: Verify the degree parameter

   To create degree 2 features, use degree=2 in the constructor.

3. Final Answer:

   from sklearn.preprocessing import PolynomialFeatures poly = PolynomialFeatures(degree=2) -> Option A

4. Quick Check:

   Import from preprocessing and set degree=2 [OK]

Hint: Import from preprocessing and set degree=2 [OK]

Common Mistakes:

• Importing from wrong module
• Forgetting 'degree=' keyword
• Setting wrong degree value

3. Given the code below, what is the output of X_poly?

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

medium

A. [[2 3 5 6 9]]

B. [[1 2 3 4 6 9]]

C. [[2 3 4 6 9]]

D. [[2 3 4 5 6 9]]

Solution

1. Step 1: Understand PolynomialFeatures output with degree=2 and include_bias=False

   Features include original features, their squares, and pairwise products: [x1, x2, x1^2, x1*x2, x2^2].

2. Step 2: Calculate values for X = [2, 3]

   x1=2, x2=3; x1^2=4, x1*x2=6, x2^2=9; so output is [[2, 3, 4, 6, 9]].

3. Final Answer:

   [[2 3 4 6 9]] -> Option C

4. Quick Check:

   Polynomial features = original + squares + products [OK]

Hint: Output includes original, squares, and cross-products [OK]

Common Mistakes:

• Including bias term when include_bias=False
• Miscomputing squares or products
• Adding extra features not in degree 2

4. Identify the error in the following code snippet that uses PolynomialFeatures:

from sklearn.preprocessing import PolynomialFeatures
X = [[1, 2], [3, 4]]
poly = PolynomialFeatures(degree=3)
X_poly = poly.fit_transform(X)
print(X_poly)

medium

A. X should be a NumPy array, not a list of lists

B. No error; code runs correctly

C. Missing import for NumPy

D. Degree 3 is not supported by PolynomialFeatures

Solution

1. Step 1: Check input type compatibility

   PolynomialFeatures accepts lists or arrays, so X as list of lists is valid.

2. Step 2: Verify degree parameter and imports

   Degree 3 is supported; no NumPy import needed if not used explicitly.

3. Final Answer:

   No error; code runs correctly -> Option B

4. Quick Check:

   PolynomialFeatures accepts lists and degree 3 [OK]

Hint: PolynomialFeatures accepts lists; degree 3 is valid [OK]

Common Mistakes:

• Assuming input must be NumPy array
• Thinking degree 3 is invalid
• Expecting import errors without NumPy usage

5. You have a dataset with 3 features and want to add polynomial features up to degree 3. How many features will the transformed dataset have if include_bias=False?

hard

A. 10

B. 20

C. 16

D. 19

Solution

1. Step 1: Use formula for number of polynomial features

   Number of features = C(n + d, d) - 1 if include_bias=False, where n=3, d=3.

2. Step 2: Calculate combinations

   C(3+3, 3) = C(6, 3) = 20; subtract 1 for no bias gives 19 features.

3. Final Answer:

   19 -> Option D

4. Quick Check:

   Features = combinations(6,3)-1 = 19 [OK]

Hint: Use combinations(n+d, d) minus bias if excluded [OK]

Common Mistakes:

• Forgetting to subtract bias feature
• Using wrong combination formula
• Confusing degree with number of features