- Load a CSV with student study hours and marks. Predict the score for a new student who studied 7 hours.
- Build a multiple linear regression model to predict house prices using area, number of bedrooms, and distance from city center.
- Calculate the Mean Squared Error manually for a small dataset and compare it with the model’s MSE.
Challenge 1: Predict Student Score for 7 Hours of Study
Linear Regression Equation: y=5.94x+29.15
Predicted Score (using model):≈ 70.74 marks
Manual Calculation (using y = mx + c): y=5.94×7+29.15 = 70.74
Challenge 2: Multiple Linear Regression for House Prices
If a house has:
- Area = 1800 sq ft
- Bedrooms = 3
- Distance = 4 km
Price= 100,000 + 100×1800 + 50,000×3 + 0×4 =430,000
Final Predicted Price = $430,000
| Term | Value Used | Why This Value Was Chosen |
|---|---|---|
| Intercept (b₀) | 100,000 | Learned by the model during training. It’s the base price when all inputs are 0. |
| Area | 1800 | A realistic mid-range house area (sq ft) between 1000–2500 in the dataset. |
| Coefficient for Area | 100 | The model learned that for every 1 sq ft increase in area, price goes up by $100. |
| Bedrooms | 3 | A typical value from the dataset (ranging 2–4). Chosen to test an average case. |
| Coefficient for Bedrooms | 50,000 | The model learned that each additional bedroom adds $50,000 in value. |
| Distance from city | 4 | An arbitrary, realistic test value (between 2–8 in the dataset). |
| Coefficient for Distance | 0 | The model found that distance had no impact on price in the dataset (coefficient = 0). |
Challenge 3: Mean Squared Error (MSE) Comparison
Actual Values: [100, 150, 200]
Predicted Values: [110, 140, 195]
Step-by-Step Residuals (Actual – Predicted):
- 100 – 110 = -10
- 150 – 140 = 10
- 200 – 195 = 5
Squared Errors:
- (-10)² = 100
- (10)² = 100
- (5)² = 25
Manual Mean Squared Error (MSE): MSE=100+100+253=75.0
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