Module 06: Linear Regression - Participation Exercises

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Module 06: Linear Regression - Participation Exercises#

Exercise 6.1: Critique - Coefficient Interpretation#

Type: 🔍 Critique (5 min)

A colleague shows you their regression model and says: “Temperature has a coefficient of 0.002, and pressure has a coefficient of 5.3. Clearly pressure is way more important!”

Task: Write 2-3 sentences explaining why this interpretation might be wrong and what they should do instead.

Your critique:

Exercise 6.2: Mini-Exercise - Diagnose the Model#

Type: 🔧 Mini-Exercise (7 min)

Look at these residual plots and diagnose what’s wrong with each model.

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(42)
n = 100
y_pred = np.linspace(0, 100, n)

# Three different residual patterns
fig, axes = plt.subplots(1, 3, figsize=(15, 4))

# Pattern A: Curved residuals
residuals_A = (y_pred - 50)**2 / 100 + np.random.normal(0, 2, n)
axes[0].scatter(y_pred, residuals_A, alpha=0.6)
axes[0].axhline(0, color='r', linestyle='--')
axes[0].set_title('Model A')
axes[0].set_xlabel('Predicted')
axes[0].set_ylabel('Residual')

# Pattern B: Fan shape
residuals_B = np.random.normal(0, y_pred/10 + 0.5, n)
axes[1].scatter(y_pred, residuals_B, alpha=0.6)
axes[1].axhline(0, color='r', linestyle='--')
axes[1].set_title('Model B')
axes[1].set_xlabel('Predicted')

# Pattern C: Good residuals
residuals_C = np.random.normal(0, 3, n)
axes[2].scatter(y_pred, residuals_C, alpha=0.6)
axes[2].axhline(0, color='r', linestyle='--')
axes[2].set_title('Model C')
axes[2].set_xlabel('Predicted')

plt.tight_layout()
plt.show()

# TASK: For each model, identify:
# 1. What pattern do you see?
# 2. What does it indicate?
# 3. How would you fix it?
../_images/233706202a076af6b18ef8f0a44b9e9f2f9d39cbeacae5e62040eca0dbdff8fe.png

Your diagnosis:

Model A:

  • Pattern:

  • Problem:

  • Fix:

Model B:

  • Pattern:

  • Problem:

  • Fix:

Model C:

  • Pattern:

  • Problem:

  • Fix:

Exercise 6.3: Reflection - Causation vs Correlation#

Type: 🤔 Reflection (3 min)

Your regression model shows that “catalyst age” has a negative coefficient for yield. A manager suggests: “Let’s always use fresh catalyst!”

Reflect:

  1. Does the coefficient prove that old catalyst causes lower yields?

  2. What else might explain the relationship?

  3. What would you need to establish causation?

Your reflection:

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