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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a polynomial feature transformer.

ML Python

from sklearn.preprocessing import [1]
poly = PolynomialFeatures(degree=2)

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

APolynomialFeatures

BStandardScaler

CMinMaxScaler

DOneHotEncoder

Attempts:

3 left

💡 Hint

Common Mistakes

Using scalers or encoders instead of polynomial feature transformer.

The PolynomialFeatures class generates polynomial and interaction features, which help regression models capture non-linear relationships.

2fill in blank

medium

Complete the code to fit a linear regression model on polynomial features.

ML Python

from sklearn.linear_model import LinearRegression
model = LinearRegression()
X_poly = poly.fit_transform(X)
model.[1](X_poly, y)

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Afit

Btransform

Cscore

Dpredict

Attempts:

3 left

💡 Hint

Common Mistakes

Using predict instead of fit to train the model.

The fit method trains the model on the transformed polynomial features and target values.

3fill in blank

hard

Fix the error in the code to predict using the polynomial regression model.

ML Python

X_new_poly = poly.transform(X_new)
predictions = model.[1](X_new_poly)

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Atransform

Bpredict

Cfit

Dscore

Attempts:

3 left

💡 Hint

Common Mistakes

Using fit or transform instead of predict for predictions.

The predict method generates predictions from the trained model using new polynomial features.

4fill in blank

hard

Fill both blanks to create a dictionary of feature names and their coefficients from the model.

ML Python

feature_names = poly.get_feature_names_out(input_features)
coef_dict = [1](zip(feature_names, model.[2]_))

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Adict

Bcoef

Ccoef_

Dlist

Attempts:

3 left

💡 Hint

Common Mistakes

Using coef without underscore or wrong function to create dictionary.

The dict function creates a dictionary from zipped feature names and coefficients stored in coef_.

5fill in blank

hard

Fill both blanks to compute the mean squared error of the polynomial regression model predictions.

ML Python

from sklearn.metrics import [1]
y_pred = model.predict(X_poly)
mse = [2](y, y_pred)
print('Mean Squared Error:', mse)

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

Amean_squared_error

Baccuracy_score

Cr2_score

Dconfusion_matrix

Attempts:

3 left

💡 Hint

Common Mistakes

Using classification metrics like accuracy or confusion matrix for regression.

The mean_squared_error function calculates the average squared difference between actual and predicted values, a common regression metric.

Practice

1. Why do advanced regression models handle non-linearity better than simple linear regression?

easy

A. Because they only use one feature at a time

B. Because they ignore data points that don't fit a line

C. Because they can model complex curved relationships in data

D. Because they always use fewer data points

Solution

1. Step 1: Understand simple linear regression limits

   Simple linear regression fits a straight line, so it cannot capture curves or bends in data.

2. Step 2: Recognize advanced regression capabilities

   Advanced regression models like decision trees or polynomial regression can fit curves and complex patterns.

3. Final Answer:

   Because they can model complex curved relationships in data -> Option C

4. Quick Check:

   Advanced regression models handle curves [OK]

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

Common Mistakes:

• Thinking advanced regression ignores data points
• Believing advanced regression uses fewer data points
• Assuming advanced regression only uses one feature

2. Which of the following is the correct way to create a polynomial regression model in Python using scikit-learn?

easy

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

B. from sklearn.tree import DecisionTreeRegressor; model = DecisionTreeRegressor(); model.fit(X, y)

C. from sklearn.cluster import KMeans; model = KMeans(); model.fit(X)

D. from sklearn.linear_model import LinearRegression; model = LinearRegression(); model.fit(X_poly, y)

Solution

1. Step 1: Identify polynomial feature creation

   Polynomial regression requires transforming features using PolynomialFeatures to add powers of features.

2. Step 2: Recognize correct syntax for polynomial transformation

   from sklearn.preprocessing import PolynomialFeatures; poly = PolynomialFeatures(degree=2); X_poly = poly.fit_transform(X) correctly imports PolynomialFeatures and transforms X to X_poly for regression.

3. Final Answer:

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

4. Quick Check:

   PolynomialFeatures creates polynomial features [OK]

Hint: Polynomial regression needs PolynomialFeatures to transform data [OK]

Common Mistakes:

• Confusing decision tree with polynomial regression
• Using clustering models for regression tasks
• Not transforming features before fitting polynomial regression

3. Given the code below, what will be the output of print(predictions)?

from sklearn.tree import DecisionTreeRegressor
X = [[1], [2], [3], [4], [5]]
y = [1, 4, 9, 16, 25]
model = DecisionTreeRegressor()
model.fit(X, y)
predictions = model.predict([[6]])
print(predictions)

medium

A. [16]

B. [36]

C. [9]

D. [25]

Solution

1. Step 1: Understand decision tree prediction behavior

   Decision trees predict by assigning the output of the closest training leaf node, not extrapolating beyond training data.

2. Step 2: Check training data and prediction input

   Input 6 is beyond training max 5, so prediction will be the leaf value for closest known input, which is 5 with output 25.

3. Final Answer:

   [25] -> Option D

4. Quick Check:

   Decision tree predicts closest leaf value = 25 [OK]

Hint: Decision trees do not extrapolate; predict closest known value [OK]

Common Mistakes:

• Assuming decision tree extrapolates like polynomial regression
• Expecting exact square of 6 (36) as output
• Confusing prediction with training labels

4. The following code tries to fit a polynomial regression but gives an error. What is the mistake?

from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
X = [[1], [2], [3], [4]]
y = [1, 4, 9, 16]
model = LinearRegression()
X_poly = PolynomialFeatures(degree=2)
model.fit(X_poly, y)

medium

A. LinearRegression cannot fit polynomial data

B. X_poly is a class, not transformed data; need to call fit_transform on X

C. y should be a 2D array, not 1D

D. Degree should be 1 for polynomial features

Solution

1. Step 1: Identify how PolynomialFeatures is used

   PolynomialFeatures is a transformer class; it needs to be applied to X using fit_transform to create polynomial features.

2. Step 2: Spot the error in code

   Code assigns X_poly to the class instance, not the transformed data. The model.fit expects numeric array, not a class object.

3. Final Answer:

   X_poly is a class, not transformed data; need to call fit_transform on X -> Option B

4. Quick Check:

   Call fit_transform on X before fitting model [OK]

Hint: Call fit_transform on X before fitting model [OK]

Common Mistakes:

• Passing transformer class instead of transformed data
• Thinking LinearRegression can't fit polynomial features
• Misunderstanding y shape requirements

5. You have a dataset where the target variable changes in a complex curve with two features. Which approach best handles this non-linearity and why?

hard

A. Polynomial regression of degree 3 can model complex curves with multiple features

B. Simple linear regression will miss the curve

C. Decision tree with max depth 2 is too shallow to capture complexity

D. Dropping features reduces information and won't help non-linearity

Solution

1. Step 1: Analyze model capabilities for non-linearity

   Simple linear regression cannot model curves; decision tree with low depth may underfit; dropping features loses info.

2. Step 2: Evaluate polynomial regression for multiple features

   Polynomial regression with degree 3 creates interaction and power terms, capturing complex curves in multiple features.

3. Final Answer:

   Polynomial regression of degree 3 can model complex curves with multiple features -> Option A

4. Quick Check:

   Degree 3 polynomial regression models complex curves [OK]

Hint: Higher degree polynomial regression models complex curves well [OK]

Common Mistakes:

• Choosing shallow decision trees that underfit
• Dropping features reduces model power
• Using simple linear regression for curved data