W Code - Pattern-Based DSA Learning Platform

Bhanu Bisht

Linear Regression

The foundation of supervised learning: Fitting lines and minimizing errors

Topics

Math + Code

Approach

🏠 Indian Context

All examples use Delhi NCR real estate data — predict flat prices based on Area, Bedrooms, Age of property, and Floor number!

What is Linear Regression?

Foundation

📊 Visual Diagram

📈 Best Fit Line (Linear Regression)

Python Implementation

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression

# Delhi NCR Flat Prices Dataset
# Feature: Area (sqft), Target: Price (Lakhs)
area = np.array([500, 800, 1000, 1200, 1500, 1800, 2000, 2500]).reshape(-1, 1)
price = np.array([25, 40, 52, 60, 78, 95, 108, 135])

# Train the model
model = LinearRegression()
model.fit(area, price)

# Get learned parameters
w = model.coef_[0]      # Weight (slope)
b = model.intercept_    # Bias (intercept)

print("=" * 50)
print("📐 LEARNED LINEAR EQUATION")
print("=" * 50)
print(f"ŷ = {w:.4f} × Area + {b:.2f}")
print(f"\nInterpretation:")
print(f"- Every 1 sqft increase → ₹{w*100:.0f} increase in price")
print(f"- Base price (intercept): ₹{b:.2f} Lakhs")

# Make prediction
new_flat = np.array([[1800]])
predicted_price = model.predict(new_flat)[0]
print(f"\n🏠 Prediction for 1800 sqft flat: ₹{predicted_price:.2f} Lakhs")

# Visualize the best-fit line
plt.figure(figsize=(10, 6))
plt.scatter(area, price, color='blue', s=100, label='Actual Data', zorder=5)
plt.plot(area, model.predict(area), color='red', linewidth=2, label=f'Best Fit: ŷ = {w:.2f}x + {b:.2f}')
plt.xlabel('Area (sqft)', fontsize=12)
plt.ylabel('Price (Lakhs)', fontsize=12)
plt.title('Linear Regression: Delhi NCR Flat Prices', fontsize=14)
plt.legend()
plt.grid(True, alpha=0.3)
# plt.show()

Key Takeaways

Linear Regression finds the best straight line through data points

Equation: ŷ = wx + b (w = slope/weight, b = intercept/bias)

Weight (w) tells how much output changes per unit input change

Bias (b) is the predicted value when all inputs are zero

import numpy as np import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression # Delhi NCR Flat Prices Dataset # Feature: Area (sqft), Target: Price (Lakhs) area = np.array([500, 800, 1000, 1200, 1500, 1800, 2000, 2500]).reshape(-1, 1) price = np.array([25, 40, 52, 60, 78, 95, 108, 135]) # Train the model model = LinearRegression() model.fit(area, price) # Get learned parameters w = model.coef_[0] # Weight (slope) b = model.intercept_ # Bias (intercept) print("=" * 50) print("📐 LEARNED LINEAR EQUATION") print("=" * 50) print(f"ŷ = {w:.4f} × Area + {b:.2f}") print(f"\nInterpretation:") print(f"- Every 1 sqft increase → ₹{w*100:.0f} increase in price") print(f"- Base price (intercept): ₹{b:.2f} Lakhs") # Make prediction new_flat = np.array([[1800]]) predicted_price = model.predict(new_flat)[0] print(f"\n🏠 Prediction for 1800 sqft flat: ₹{predicted_price:.2f} Lakhs") # Visualize the best-fit line plt.figure(figsize=(10, 6)) plt.scatter(area, price, color='blue', s=100, label='Actual Data', zorder=5) plt.plot(area, model.predict(area), color='red', linewidth=2, label=f'Best Fit: ŷ = {w:.2f}x + {b:.2f}') plt.xlabel('Area (sqft)', fontsize=12) plt.ylabel('Price (Lakhs)', fontsize=12) plt.title('Linear Regression: Delhi NCR Flat Prices', fontsize=14) plt.legend() plt.grid(True, alpha=0.3) # plt.show()