Multiple linear regression in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the linear regression model from scikit-learn.

ML Python

from sklearn.linear_model import [1]

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

AKNeighborsClassifier

BLogisticRegression

CDecisionTreeRegressor

DLinearRegression

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing classification models like LogisticRegression instead of LinearRegression.

Using tree-based models which are not linear regression.

The LinearRegression class is used for multiple linear regression in scikit-learn.

2fill in blank

medium

Complete the code to create a linear regression model instance.

ML Python

model = [1]()

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

ARandomForestRegressor

BLogisticRegression

CLinearRegression

DKMeans

Attempts:

3 left

💡 Hint

Common Mistakes

Using classification or clustering models instead of linear regression.

Forgetting to add parentheses to create an instance.

We create an instance of LinearRegression to train a multiple linear regression model.

3fill in blank

hard

Fix the error in the code to train the model with features X and target y.

ML Python

model.fit([1], y)

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

AX

By

Cmodel

Dfit

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the order of features and target in the fit method.

Passing the model or method name instead of data.

The fit method requires the features as the first argument and the target as the second.

4fill in blank

hard

Fill both blanks to predict target values and calculate the mean squared error.

ML Python

predictions = model.[1](X_test)
mse = mean_squared_error(y_test, [2])

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

Apredict

Bpredictions

Cfit

DX_test

Attempts:

3 left

💡 Hint

Common Mistakes

Using fit instead of predict for predictions.

Passing features instead of predictions to the error function.

Use predict to get predictions from the model, then pass those predictions to mean_squared_error to calculate error.

5fill in blank

hard

Fill all three blanks to create a dictionary of coefficients, intercept, and R² score.

ML Python

results = {
    'coefficients': model.[1],
    'intercept': model.[2],
    'r2_score': model.[3](X_test, y_test)
}

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

Acoef_

Bintercept_

Cscore

Dfit

Attempts:

3 left

💡 Hint

Common Mistakes

Using method names instead of attributes for coefficients and intercept.

Confusing fit with score.

The model's coefficients are in coef_, intercept in intercept_, and score computes the R² on test data.

Practice

1. What does multiple linear regression do in simple terms?

easy

A. It predicts a result using several input features combined.

B. It groups data into clusters based on similarity.

C. It reduces the number of features by combining them.

D. It finds the shortest path between two points.

Solution

1. Step 1: Understand the purpose of multiple linear regression

   Multiple linear regression uses multiple inputs to predict a single output by finding the best weights for each input.

2. Step 2: Compare options with this understanding

   Only It predicts a result using several input features combined. correctly describes predicting a result using several inputs combined.

3. Final Answer:

   It predicts a result using several input features combined. -> Option A

4. Quick Check:

   Multiple inputs predict output = A [OK]

Hint: Remember: multiple inputs, one output prediction [OK]

Common Mistakes:

• Confusing regression with clustering
• Thinking it reduces features instead of weighting them
• Mixing it up with pathfinding algorithms

2. Which of the following is the correct formula for multiple linear regression prediction?

easy

A. y = w0 + w1*x1 + w2*x2 + ... + wn*xn

B. y = w0 * x1 + w1 * x2 + ... + wn * xn

C. y = w0 / x1 + w1 / x2 + ... + wn / xn

D. y = w0 - w1*x1 - w2*x2 - ... - wn*xn

Solution

1. Step 1: Recall the multiple linear regression formula

   The prediction is a sum of a bias term plus each input multiplied by its weight: y = w0 + w1*x1 + w2*x2 + ... + wn*xn.

2. Step 2: Check each option against the formula

   Only y = w0 + w1*x1 + w2*x2 + ... + wn*xn matches the correct formula with addition and multiplication.

3. Final Answer:

   y = w0 + w1*x1 + w2*x2 + ... + wn*xn -> Option A

4. Quick Check:

   Sum of weighted inputs plus bias = B [OK]

Hint: Sum weighted inputs plus bias for prediction [OK]

Common Mistakes:

• Using multiplication instead of addition between terms
• Dividing weights by inputs
• Subtracting weights instead of adding

3. Given weights w0=2, w1=3, w2=-1 and inputs x1=4, x2=5, what is the predicted value y using multiple linear regression?

medium

A. 9.5

B. 9

C. 5

D. 10

Solution

1. Step 1: Apply the formula y = w0 + w1*x1 + w2*x2

   Substitute values: y = 2 + 3*4 + (-1)*5.

2. Step 2: Calculate the prediction

   Calculate: 3*4 = 12, (-1)*5 = -5, sum = 2 + 12 - 5 = 9.

3. Step 3: Recheck calculation

   Sum is 9, but 10 says 10, so re-check: 2 + 12 - 5 = 9, so correct answer is 9.

4. Final Answer:

   9 -> Option B

5. Quick Check:

   2 + 12 - 5 = 9 [OK]

Hint: Multiply weights by inputs, then add bias [OK]

Common Mistakes:

• Adding weights instead of multiplying by inputs
• Forgetting to add bias term w0
• Mixing up signs of weights

4. Identify the error in this Python code for multiple linear regression prediction:

def predict(x1, x2, w0, w1, w2):
    return w0 + w1 * x1 + w2 + x2

print(predict(3, 4, 1, 2, 3))

medium

A. The print statement syntax is incorrect.

B. The function is missing a return statement.

C. The function parameters are in wrong order.

D. The term w2 + x2 should be w2 * x2 for correct multiplication.

Solution

1. Step 1: Analyze the formula inside the function

   The formula should multiply each input by its weight: w0 + w1*x1 + w2*x2.

2. Step 2: Identify the mistake in the code

   The code uses w2 + x2 instead of w2 * x2, which adds instead of multiplies.

3. Final Answer:

   The term w2 + x2 should be w2 * x2 for correct multiplication. -> Option D

4. Quick Check:

   Multiplication needed, not addition = A [OK]

Hint: Check all input-weight pairs use multiplication [OK]

Common Mistakes:

• Using + instead of * between weight and input
• Forgetting return statement (not here though)
• Mixing parameter order
• Incorrect print syntax

5. You have a dataset with features: hours studied (x1), hours slept (x2), and exam score (y). You fit a multiple linear regression model and get weights: w0=5, w1=4, w2=2. What does the weight w1=4 tell you about hours studied?

hard

A. Hours slept affects exam score more than hours studied.

B. Hours studied has no effect on exam score.

C. For each extra hour studied, exam score increases by 4 points, holding sleep constant.

D. Exam score decreases by 4 points for each hour studied.

Solution

1. Step 1: Understand the meaning of weights in multiple linear regression

   Each weight shows how much the output changes when that input increases by one unit, keeping others fixed.

2. Step 2: Interpret w1=4 for hours studied

   A weight of 4 means exam score increases by 4 points for each additional hour studied, assuming hours slept stays the same.

3. Final Answer:

   For each extra hour studied, exam score increases by 4 points, holding sleep constant. -> Option C

4. Quick Check:

   Weight shows effect per unit input = D [OK]

Hint: Weight = change in output per unit input [OK]

Common Mistakes:

• Thinking weight means no effect
• Confusing positive and negative effect
• Mixing effects of different features