Regression evaluation (MSE, RMSE, R²) in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate Mean Squared Error (MSE) between true and predicted values.

ML Python

from sklearn.metrics import mean_squared_error
mse = mean_squared_error(y_true, [1])

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

Ay_pred

By_train

Cy_test

Dy_score

Attempts:

3 left

💡 Hint

Common Mistakes

Using training labels instead of predicted values.

Confusing variable names for predictions.

The Mean Squared Error function compares the true values y_true with the predicted values y_pred.

2fill in blank

medium

Complete the code to calculate Root Mean Squared Error (RMSE) from MSE.

ML Python

import numpy as np
rmse = np.sqrt([1])

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

Amean_absolute_error(y_true, y_pred)

Bmean_squared_error(y_true, y_pred)

Cr2_score(y_true, y_pred)

Daccuracy_score(y_true, y_pred)

Attempts:

3 left

💡 Hint

Common Mistakes

Using mean absolute error or R² score instead of MSE.

Forgetting to take the square root.

RMSE is the square root of the Mean Squared Error (MSE), so we pass MSE inside np.sqrt().

3fill in blank

hard

Fix the error in the code to calculate R² score correctly.

ML Python

from sklearn.metrics import r2_score
score = r2_score([1], y_pred)

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

Ay_true

By_train

Cy_pred

Dy_test

Attempts:

3 left

💡 Hint

Common Mistakes

Passing predicted values as the first argument.

Mixing training and test sets.

The R² score function compares the true values y_true with predicted values y_pred.

4fill in blank

hard

Fill both blanks to compute RMSE using MSE stored in variable mse.

ML Python

import numpy as np
rmse = np.[1]([2])

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

Asqrt

Bmean

Cmse

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.mean or np.sum instead of np.sqrt.

Passing wrong variable instead of mse.

RMSE is the square root of the MSE value stored in mse. Use np.sqrt(mse).

5fill in blank

hard

Fill all three blanks to create a dictionary with R² score and RMSE from predictions.

ML Python

from sklearn.metrics import r2_score, mean_squared_error
import numpy as np
results = {
    '[1]': r2_score(y_true, y_pred),
    '[2]': np.sqrt(mean_squared_error(y_true, y_pred)),
    '[3]': mean_squared_error(y_true, y_pred)
}

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

AR2

BRMSE

CMSE

DAccuracy

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect or inconsistent dictionary keys.

Mixing metric names with unrelated terms.

The dictionary keys should be R2 for R² score, RMSE for root mean squared error, and MSE for mean squared error.

Practice

1. What does the Mean Squared Error (MSE) measure in regression evaluation?

easy

A. The total number of data points

B. The average of the squared differences between predicted and actual values

C. The correlation between features

D. The percentage of correct predictions

Solution

1. Step 1: Understand MSE definition

   MSE calculates the average of squared differences between predicted and actual values to measure error size.

2. Step 2: Compare options to definition

   Only The average of the squared differences between predicted and actual values correctly describes MSE as average squared error; others describe unrelated concepts.

3. Final Answer:

   The average of the squared differences between predicted and actual values -> Option B

4. Quick Check:

   MSE = average squared error [OK]

Hint: MSE = average squared error between prediction and truth [OK]

Common Mistakes:

• Confusing MSE with accuracy
• Thinking MSE measures correlation
• Mixing MSE with count of data points

2. Which of the following Python code snippets correctly calculates the Root Mean Squared Error (RMSE) given true values y_true and predicted values y_pred?

easy

A. rmse = np.sum((y_true - y_pred)**2)

B. rmse = np.mean(np.abs(y_true - y_pred))

C. import numpy as np
rmse = np.sqrt(np.mean((y_true - y_pred)**2))

D. rmse = np.sqrt(np.sum(y_true - y_pred))

Solution

1. Step 1: Recall RMSE formula

   RMSE is the square root of the mean of squared differences between true and predicted values.

2. Step 2: Match code to formula

   import numpy as np rmse = np.sqrt(np.mean((y_true - y_pred)**2)) correctly computes squared differences, averages them, then takes square root. Others miss steps or use wrong operations.

3. Final Answer:

   import numpy as np rmse = np.sqrt(np.mean((y_true - y_pred)**2)) -> Option C

4. Quick Check:

   RMSE = sqrt(mean squared error) [OK]

Hint: RMSE = sqrt of mean squared error, use np.sqrt(np.mean(...)) [OK]

Common Mistakes:

• Using sum instead of mean
• Taking sqrt before mean
• Using absolute difference instead of squared

3. Given the true values y_true = [3, -0.5, 2, 7] and predicted values y_pred = [2.5, 0.0, 2, 8], what is the R² score?

medium

A. 1.0

B. 0.865

C. 0.75

D. 0.948

Solution

1. Step 1: Calculate R² score formula

   R² = 1 - (sum of squared residuals / total sum of squares). Calculate residuals and totals:

2. Step 2: Compute sums

   Residuals squared: (3-2.5)^2 + (-0.5-0)^2 + (2-2)^2 + (7-8)^2 = 0.25 + 0.25 + 0 + 1 = 1.5
   Total sum squares: sum((y_true - mean(y_true))^2) with mean= (3-0.5+2+7)/4=2.875
   Totals: (3-2.875)^2 + (-0.5-2.875)^2 + (2-2.875)^2 + (7-2.875)^2 = 0.015625 + 11.390625 + 0.765625 + 17.015625 = 29.1875

3. Step 3: Calculate R²

   R² = 1 - (1.5 / 29.1875) ≈ 1 - 0.0514 = 0.9486

4. Final Answer:

   0.948 -> Option D

5. Quick Check:

   R² ≈ 0.95 means good fit [OK]

Hint: R² = 1 - (SS_res / SS_tot), calculate sums carefully [OK]

Common Mistakes:

• Using sum of residuals instead of squared residuals
• Forgetting to subtract mean in total sum squares
• Mixing up numerator and denominator

4. You have this Python code to compute MSE but it gives wrong results:

def mse(y_true, y_pred):
    return sum(y_true - y_pred)**2 / len(y_true)

What is the error?

medium

A. The subtraction is done element-wise but sum is outside, causing wrong squaring

B. The function should use absolute values instead of squares

C. The length should be squared, not the sum

D. The function is missing import statements

Solution

1. Step 1: Analyze the code operation order

   The code does sum(y_true - y_pred) first, then squares the total sum, which is incorrect for MSE.

2. Step 2: Correct MSE calculation

   MSE requires squaring each difference first, then averaging. The code should square element-wise before summing.

3. Final Answer:

   The subtraction is done element-wise but sum is outside, causing wrong squaring -> Option A

4. Quick Check:

   Square differences before sum for MSE [OK]

Hint: Square each difference before summing for MSE [OK]

Common Mistakes:

• Squaring sum instead of sum of squares
• Using absolute difference instead of squared
• Ignoring element-wise operations

5. You trained two regression models on different datasets. Model A has MSE=4 and R²=0.8, Model B has MSE=2 and R²=0.6. Which model is better and why?

hard

A. Model B is better because it has lower MSE, indicating smaller average error

B. Model A is better because it has higher R², showing better fit to data

C. Both models are equally good because MSE and R² contradict

D. Cannot decide without RMSE values

Solution

1. Step 1: Understand MSE and R² meanings

   MSE measures average squared error (lower is better). R² measures proportion of variance explained (higher is better).

2. Step 2: Compare models on error and fit

   Model B has lower MSE (2 < 4), so predictions are closer on average. Model A has higher R² but larger error, meaning it fits variance better but with bigger errors.

3. Step 3: Prioritize error for prediction quality

   Lower error (MSE) usually means better prediction accuracy, so Model B is better despite lower R².

4. Final Answer:

   Model B is better because it has lower MSE, indicating smaller average error -> Option A

5. Quick Check:

   Lower MSE means better prediction accuracy [OK]

Hint: Lower MSE beats higher R² for prediction accuracy [OK]

Common Mistakes:

• Choosing model with higher R² ignoring error size
• Thinking MSE and R² always agree
• Ignoring what metric matters for task