Practice Problems & Self-Assessment

Overview

This section contains 95+ practice problems spanning all CT exam topics. Each problem is designed to reinforce concepts, build calculation skills, and improve exam performance.

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Problem Categories

Category	Count	Difficulty	Est. Time	Topics
Module 1 Basics	8	Easy-Medium	60 min	Linear Regression, Simple relationships
Module 1 Advanced	22	Medium-Hard	180 min	Multiple Reg, Bias-Variance, Metrics
Module 2 Foundations	18	Easy-Medium	120 min	CV, Logistic basics
Module 2 Advanced	22	Medium-Hard	180 min	ROC, Metrics, Model selection
Real-World Scenarios	15	Hard	150 min	Business problems, end-to-end
Critical Thinking	10	Hard	100 min	Trade-offs, design decisions
Total	95	Mixed	790 min (13 hrs)	All topics

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Difficulty Breakdown

Easy (25-27 problems, 26-28%):
  • Basic calculations (SSE, RMSE, accuracy)
  • Fundamental concepts (what is overfitting?)
  • No complex interpretation required
  • Estimated time: 5-15 minutes each

Medium (48-50 problems, 50-53%):
  • Multi-step problems (calculate then interpret)
  • Model comparison (which is better?)
  • Practical scenarios with data
  • Estimated time: 15-25 minutes each

Hard (18-22 problems, 19-23%):
  • End-to-end workflows
  • Trade-off analysis and design decisions
  • Debugging and diagnosis
  • Real-world constraints and costs
  • Estimated time: 20-30 minutes each

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How to Use These Problems

🎯 Study Strategy (3 Phases)

Phase 1: Attempt (No peeking at solutions)

1. Pick a problem at your current difficulty level
2. Set a timer (see estimated time)
3. Attempt without looking at solution
4. Write down your reasoning

Phase 2: Self-Grade

1. Check your answer against solution
2. Note if you got it right/wrong
3. Read the "Common Mistakes" section
4. Identify where you went wrong

Phase 3: Reinforce

1. Return to concept page if confused
2. Review the solution explanation
3. Try a similar problem
4. Mark topic as "mastered" or "needs work"

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Problem Organization

📚 Module 1 Problems (30 problems, 4-5 hours)

Linear Regression (8 problems)

• Problem 1.1: Calculate slope and intercept
• Problem 1.2: Compute SSE, MSE, RMSE from residuals
• Problem 1.3: Interpret regression coefficients
• Problem 1.4: Prediction and confidence interval
• Problem 1.5-1.8: Mixed application problems

Multiple Regression (7 problems)

• Problem 2.1: Compare simple vs multiple regression
• Problem 2.2: Interpret partial coefficients
• Problem 2.3: Multicollinearity detection
• Problem 2.4: Feature scaling impact
• Problem 2.5-2.7: Model comparison

Bias-Variance (8 problems)

• Problem 3.1: Bias-variance decomposition
• Problem 3.2: Learning curves interpretation
• Problem 3.3: Cross-validation error analysis
• Problem 3.4: Regularization parameter tuning
• Problem 3.5-3.8: Diagnosis and remediation

Error Metrics (7 problems)

• Problem 4.1: MSE vs MAE comparison
• Problem 4.2: R² calculation and interpretation
• Problem 4.3: Cross-validation results
• Problem 4.4-4.7: Integrated metric problems

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🎯 Module 2 Problems (40 problems, 5-6 hours)

Cross-Validation (8 problems)

• Problem 1.1-1.3: K-fold CV calculations
• Problem 1.4: LOOCV vs K-fold comparison
• Problem 1.5: Stratified CV for imbalanced data
• Problem 1.6-1.8: Hyperparameter selection

Logistic Regression (10 problems)

• Problem 2.1: Sigmoid function properties
• Problem 2.2-2.3: Probability calculations
• Problem 2.4: Binary classification
• Problem 2.5: Multi-class OvR vs OvO
• Problem 2.6-2.10: Interpretation and application

Classification Metrics (10 problems)

• Problem 3.1: Confusion matrix construction
• Problem 3.2-3.4: Precision, Recall, F1 calculations
• Problem 3.5: ROC curve construction
• Problem 3.6: AUC calculation and interpretation
• Problem 3.7: Decision threshold tuning
• Problem 3.8-3.10: Metric selection for business problems

Model Comparison (8 problems)

• Problem 4.1: Algorithm selection framework
• Problem 4.2-4.3: Bias-variance across models
• Problem 4.4: Performance vs interpretability tradeoff
• Problem 4.5: Data size impact
• Problem 4.6-4.8: Real-world model selection

Decision Boundaries (4 problems)

• Problem 5.1: Boundary shape identification
• Problem 5.2: Overfitting vs underfitting diagnosis
• Problem 5.3-5.4: Model comparison via boundaries

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🌟 Mixed & Real-World Problems (25 problems, 3-4 hours)

Real-World Scenarios (10 problems)

• Customer Churn Prediction (Accuracy vs Recall tradeoff)
• Medical Diagnosis (Cost of false negatives)
• Fraud Detection (Class imbalance handling)
• Email Spam (Precision vs Recall choice)
• Recommendation System (Evaluation metrics)
• Credit Scoring (Fairness considerations)
• Employee Attrition (Cost-benefit analysis)
• Product Recommendation (A/B test design)
• Market Segmentation (Feature importance)
• Sentiment Analysis (Multi-class metrics)

End-to-End Pipelines (8 problems)

• Data → Preprocessing → Model → Evaluation workflow
• From problem statement to deployment decision
• Integration of multiple concepts

Critical Thinking (7 problems)

• Design trade-offs: accuracy vs speed vs cost
• What would you do if...? scenarios
• Constraint satisfaction problems
• Ethical ML considerations

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Solutions Guide

📖 Complete Solutions

All solutions include:

• ✓ Step-by-step calculations
• ✓ Reasoning for each decision
• ✓ Alternative approaches (when applicable)
• ✓ Common mistakes analysis
• ✓ Why the answer matters
• ✓ Real-world implications

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Self-Assessment Checklist

Use this to track your progress:

Module 1: Linear & Multiple Regression

• Can calculate regression coefficients from data
• Understand SSE, MSE, RMSE, and R²
• Can compare simple vs multiple regression
• Recognize multicollinearity problems
• Know when to use feature scaling

Module 1: Bias-Variance & Evaluation

• Understand bias-variance tradeoff
• Can read learning curves correctly
• Know how to interpret CV results
• Can select hyperparameters using CV
• Understand regularization (Ridge, Lasso)

Module 2: Classification Basics

• Can run K-fold cross-validation
• Understand logistic regression formula
• Can convert probability to classification
• Know binary vs multi-class approaches
• Can interpret logistic coefficients

Module 2: Classification Metrics

• Can build confusion matrix
• Know Precision, Recall, F1, and when to use each
• Can construct ROC curve
• Understand AUC and its meaning
• Can tune decision threshold

Module 2: Model Selection & Decision Boundaries

• Know algorithm selection framework
• Can compare algorithms on multiple dimensions
• Understand bias-variance for different models
• Can visualize decision boundaries
• Can diagnose overfitting via boundaries

Integration & Real-World

• Can design end-to-end classification pipeline
• Can perform cost-benefit analysis
• Can select metrics based on business problem
• Can justify algorithm choices
• Can handle trade-offs and constraints

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Tips for Success

📌 Before Starting

1. Review the concept page relevant to the problem
2. Note the difficulty level - Easy first, progress to Hard
3. Set a timer - Use estimated time as guide
4. Gather materials - Paper, pen, calculator if needed

💡 While Solving

1. Show all steps - Even if you just want the answer
2. State assumptions - "Assuming..." when data is ambiguous
3. Use proper notation - Match textbook/course style
4. Check reasonableness - Does answer make sense?

✅ When Checking

1. Compare methodology - Did you follow right approach?
2. Check arithmetic - Even small errors matter
3. Read explanation - Learn WHY answer is right
4. Review common mistakes - Don't repeat them!

📚 For Weak Areas

1. Go back to concept page - Reread theory
2. Try similar problem - Another angle on same concept
3. Change numbers - Create your own variation
4. Teach someone - Explain concept aloud

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Problem Statistics

By Topic

Topic	Easy	Medium	Hard	Total	Est. Time
Linear Regression	3	3	2	8	60 min
Multiple Regression	1	4	2	7	90 min
Bias-Variance	2	4	2	8	100 min
Metrics (Regression)	2	3	2	7	70 min
Cross-Validation	2	4	2	8	100 min
Logistic Regression	3	5	2	10	120 min
Classification Metrics	3	5	2	10	120 min
Model Comparison	2	4	2	8	100 min
Decision Boundaries	1	2	1	4	50 min
Real-World Scenarios	2	5	3	10	120 min
Pipelines	1	3	4	8	120 min
Critical Thinking	0	2	5	7	100 min
TOTAL	23	45	27	95	1190 min

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Recommended Study Paths

🎯 Path 1: Concept Mastery (4-5 weeks)

1. Week 1: Module 1 Easy problems (2-3 hours)
2. Week 2: Module 1 Medium problems (3-4 hours)
3. Week 3: Module 2 Easy/Medium problems (3-4 hours)
4. Week 4: Module 2 Medium problems (3-4 hours)
5. Week 5: Hard problems + Real-world (4-5 hours)

🎯 Path 2: Intensive Prep (1-2 weeks)

1. Day 1-2: Module 1 all difficulty (5-6 hours)
2. Day 3-4: Module 2 all difficulty (6-7 hours)
3. Day 5-7: Hard problems + Real-world (6-8 hours)
4. Day 8-10: Timed practice + review (8-10 hours)

🎯 Path 3: Quick Review (1 week)

1. Easy problems from all topics (3-4 hours)
2. Medium problems from weak areas (3-4 hours)
3. Hard + Real-world problems (4-5 hours)
4. Timed mock exam (2-3 hours)

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Problem Features

Each problem includes:

✓ Clear problem statement - Context and specific questions
✓ Relevant data - All numbers provided
✓ Sub-questions - Usually 3-5 parts building in complexity
✓ Solution with steps - How to get from data to answer
✓ Common mistakes - Why students usually get it wrong
✓ Concept link - Which page to review if stuck
✓ Time estimate - How long it typically takes
✓ Difficulty label - Easy/Medium/Hard
✓ Real-world context - Why this matters
✓ Alternative approaches - When multiple paths exist

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Get Started

Recommended first steps:

1. Take self-assessment (5 min)

   • Which topics feel strongest?
   • Which need the most work?

2. Start with Easy problems (1-2 hours)

   • Build confidence
   • Practice basic calculations
   • Get comfortable with format

3. Progress to Medium (2-3 hours)

   • Apply multiple concepts
   • Start interpreting results
   • Handle realistic scenarios

4. Master Hard problems (2-3 hours)

   • Complete workflows
   • Trade-off analysis
   • Real-world complexity

5. Timed practice (1-2 hours)

   • Simulate exam conditions
   • Aim for 80%+ accuracy within time limit

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Navigation

→ Module 1 Problems (30 problems, 4-5 hours)
→ Module 2 Problems (40 problems, 5-6 hours)
→ Mixed & Real-World Problems (25 problems, 3-4 hours)
→ Complete Solutions Guide (All answers + explanations)

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Total Practice: 95+ problems, 13+ hours of study material, complete solutions

Good luck! 🚀