Multiple Linear Regression using Scikit-Learn for House Price Prediction

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📌 Aim

To implement Multiple Linear Regression using Scikit-Learn for predicting house prices based on multiple input features.

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🎯 Objectives

• Understand Multiple Linear Regression
• Create a real-time style dataset
• Train a regression model using Scikit-Learn
• Predict house prices using multiple variables
• Evaluate model performance using:
  • Mean Squared Error (MSE)
  • R² Score
• Visualize Actual vs Predicted values

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📖 Theory

🔹 Multiple Linear Regression

Multiple Linear Regression predicts a dependent variable using multiple independent variables.

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🔹 Mathematical Model

$$\hat{y} = \theta_0 + \theta_1x_1 + \theta_2x_2 + \theta_3x_3 + \dots + \theta_nx_n$$

Where:

• $\hat{y}$ → Predicted value
• $\theta_0$ → Intercept
• $\theta_1, \theta_2, \theta_3$ → Coefficients
• $x_1, x_2, x_3$ → Input features

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📊 Real-Time Example

We predict House Price based on:

Feature	Description
Area	Size of house (sq.ft)
Bedrooms	Number of bedrooms
Age	Age of house
Distance	Distance from city center

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📋 Dataset (Randomly Generated)

Area	Bedrooms	Age	Distance	Price
1200	2	10	5	250
1500	3	5	3	320
1800	3	8	4	340
2400	4	2	2	450
3000	5	1	1	600

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📌 Algorithm

1. Import libraries
2. Create dataset
3. Split data into features and target
4. Train Multiple Linear Regression model
5. Predict values
6. Evaluate model using MSE and R²
7. Predict price for a new house
8. Visualize results

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💻 Program

# ============================================
# MULTIPLE LINEAR REGRESSION
# House Price Prediction
# ============================================

# Import libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score

# --------------------------------------------
# Create Dataset
# --------------------------------------------

data = {
    'Area': [1200, 1500, 1800, 2400, 3000,
             3500, 4000, 4500, 5000, 5500],

    'Bedrooms': [2, 3, 3, 4, 5,
                  5, 6, 6, 7, 7],

    'Age': [10, 5, 8, 2, 1,
            3, 2, 4, 1, 2],

    'Distance': [5, 3, 4, 2, 1,
                 2, 1, 3, 2, 1],

    'Price': [250, 320, 340, 450, 600,
              650, 700, 720, 800, 850]
}

# Create DataFrame
df = pd.DataFrame(data)

# Display Dataset
print("\nDATASET\n")
print(df)

# --------------------------------------------
# Prepare Input and Output
# --------------------------------------------

# Independent variables
X = df[['Area', 'Bedrooms', 'Age', 'Distance']]

# Dependent variable
y = df['Price']

# --------------------------------------------
# Build Model
# --------------------------------------------

model = LinearRegression()

# Train model
model.fit(X, y)

# --------------------------------------------
# Predictions
# --------------------------------------------

y_pred = model.predict(X)

# --------------------------------------------
# Model Parameters
# --------------------------------------------

print("\nMODEL PARAMETERS\n")

print("Intercept:")
print(model.intercept_)

print("\nCoefficients:")
for feature, coef in zip(X.columns, model.coef_):
    print(feature, ":", coef)

# --------------------------------------------
# Regression Equation
# --------------------------------------------

print("\nREGRESSION EQUATION\n")

print("Price = ")

for feature, coef in zip(X.columns, model.coef_):
    print(f"({coef:.4f} * {feature}) + ")

print(model.intercept_)

# --------------------------------------------
# Evaluation Metrics
# --------------------------------------------

mse = mean_squared_error(y, y_pred)

r2 = r2_score(y, y_pred)

print("\nEVALUATION METRICS\n")

print("Mean Squared Error (MSE):", round(mse, 4))

print("R² Score:", round(r2, 4))

# --------------------------------------------
# Predict New House Price
# --------------------------------------------

new_house = pd.DataFrame({
    'Area': [2800],
    'Bedrooms': [4],
    'Age': [2],
    'Distance': [2]
})

predicted_price = model.predict(new_house)

print("\nNEW HOUSE PREDICTION\n")

print("Predicted House Price:",
      round(predicted_price[0], 2))

# --------------------------------------------
# Visualization
# --------------------------------------------

plt.figure(figsize=(8,6))

plt.scatter(y, y_pred, color='blue')

plt.plot([y.min(), y.max()],
         [y.min(), y.max()],
         color='red')

plt.xlabel("Actual Prices")
plt.ylabel("Predicted Prices")

plt.title("Actual vs Predicted Prices")

plt.grid(True)

plt.show()

# ============================================
# END OF PROGRAM
# ============================================

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📊 Sample Output

DATASET

   Area  Bedrooms  Age  Distance  Price
0  1200         2   10         5    250
1  1500         3    5         3    320
2  1800         3    8         4    340
3  2400         4    2         2    450
4  3000         5    1         1    600
5  3500         5    3         2    650
6  4000         6    2         1    700
7  4500         6    4         3    720
8  5000         7    1         2    800
9  5500         7    2         1    850

MODEL PARAMETERS

Intercept:
151.9548847198012

Coefficients:
Area : 0.08786516356237986
Bedrooms : 36.348475116830265
Age : 0.9805984363579832
Distance : -19.51540386702398

REGRESSION EQUATION

Price = 
(0.0879 * Area) + 
(36.3485 * Bedrooms) + 
(0.9806 * Age) + 
(-19.5154 * Distance) + 
151.9548847198012

EVALUATION METRICS

Mean Squared Error (MSE): 406.4522
R² Score: 0.9901

NEW HOUSE PREDICTION

Predicted House Price: 506.3

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📈 Interpretation

Observation	Meaning
Positive coefficient	Feature increases price
Negative coefficient	Feature decreases price
Low MSE	Better prediction
R² close to 1	Strong model

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📉 Graph Explanation

Actual vs Predicted Plot

• X-axis → Actual prices
• Y-axis → Predicted prices
• Points near red line → good prediction accuracy

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🔍 Advantages of Multiple Linear Regression

• Handles multiple features
• Simple and interpretable
• Fast training
• Useful for prediction tasks

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⚠️ Limitations

• Assumes linear relationship
• Sensitive to outliers
• Multicollinearity affects performance

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✅ Result

Multiple Linear Regression was successfully implemented using Scikit-Learn to predict house prices using multiple input variables.

The experiment demonstrated how multiple input variables can be used to predict house prices effectively using Multiple Linear Regression.