Residual analysis in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Residuals in Regression

What does a residual represent in a regression model?

A The predicted value of the dependent variable

B The difference between the observed value and the predicted value

C The average value of the dependent variable

D The slope of the regression line

❓ Predict Output

intermediate

Calculate Residuals from Predictions

Given the true values and predicted values below, what is the list of residuals?

ML Python

true_values = [10, 15, 20, 25]
predicted_values = [8, 14, 22, 24]
residuals = [true - pred for true, pred in zip(true_values, predicted_values)]
print(residuals)

A [2, 1, 2, -1]

B [-2, -1, 2, -1]

C [2, -1, -2, 1]

D [2, 1, -2, 1]

❓ Metrics

advanced

Choosing the Correct Residual Metric

Which metric best summarizes the average magnitude of residuals without canceling positive and negative errors?

A Mean Residual

B Mean Squared Error (MSE)

C Mean Absolute Error (MAE)

D Residual Sum

🔧 Debug

advanced

Identify the Error in Residual Calculation Code

What error will this code produce when calculating residuals?

ML Python

true_vals = [5, 7, 9]
pred_vals = [4, 6]
residuals = [t - p for t, p in zip(true_vals, pred_vals)]
print(residuals)

A No error; outputs [1, 1]

B IndexError due to different list lengths

C TypeError due to subtraction of incompatible types

D ValueError due to zip mismatch

❓ Model Choice

expert

Model Selection Based on Residual Patterns

You observe a pattern in residuals that increases with predicted values, indicating heteroscedasticity. Which model adjustment is best to address this?

A Use weighted least squares regression giving less weight to points with larger residuals

B Switch to a linear regression without intercept

C Increase the number of features in the model

D Use a decision tree regression without residual analysis