Linear Regression Example: Predicting House Prices

In this example, we will build a **linear regression** model to predict house prices based on their size in square meters. Each step in the process will be explained in detail, showing how the data is prepared, the model is trained, and the predictions are made.

Step 1: Importing Required Libraries

First, we import the necessary Python libraries:

• NumPy: Used for handling numerical arrays.
• Matplotlib: Used for data visualization.
• scikit-learn (sklearn): Used for creating and training the regression model.
• train_test_split: Used to split the dataset into training and test sets.

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

These libraries will help us create, train, and visualize the linear regression model.

Step 2: Creating the Dataset

We create a small dataset containing **house sizes (in square meters)** and their corresponding **prices (in thousands of dollars)**. This dataset represents real estate price trends, where larger houses tend to have higher prices.

# Simulated data: house size (square meters) and price (thousands of dollars)
X = np.array([50, 60, 75, 80, 100, 120, 150, 170, 200, 220]).reshape(-1, 1)
y = np.array([150, 180, 210, 230, 280, 300, 350, 370, 400, 450])  # Price in thousands of dollars

The variable X represents house sizes, and y represents prices. We reshape X to make it compatible with the scikit-learn model.

Step 3: Splitting the Data into Training and Test Sets

To evaluate the model, we split the data into **training (80%)** and **test (20%)** sets. This ensures that the model is trained on one part of the data and tested on another to measure its accuracy.

# Split data into training (80%) and test (20%) sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

After running this cell, X_train and y_train will contain the training data, while X_test and y_test will contain the test data.

Step 4: Training the Linear Regression Model

Now, we create an instance of the **LinearRegression** model and train it using the training data. The model will learn the relationship between house size and price.

# Create and train the linear regression model
model = LinearRegression()
model.fit(X_train, y_train)

After this step, the model has learned the trend in the data and is ready to make predictions.

Step 5: Displaying the Regression Equation

Once trained, we extract the **equation of the regression line**, which helps us understand the relationship between house size and price.

# Display the regression equation
print(f"Model equation: Price = {model.coef_[0]:.2f} * Size + {model.intercept_:.2f}")

This equation shows how much the price changes for each square meter increase in house size.

Step 6: Visualizing the Regression Model

To better understand how the model fits the data, we create a **scatter plot** of the real data and overlay the **regression line**.

# Visualization of the model
plt.scatter(X, y, color="blue", label="Real Data")
plt.plot(X, model.predict(X), color="red", linewidth=2, label="Linear Regression")
plt.xlabel("Size (m²)")
plt.ylabel("Price (thousands of $)")
plt.title("Linear Regression: House Price Prediction")
plt.legend()
plt.show()

- The blue points represent actual house prices. - The red line represents the predictions made by the model. A well-fitted model should have the red line closely following the trend of the blue points.

Step 7: Predicting House Prices with User Input

Now, we allow the user to enter a house size, and the model will predict its price.

# Interactive input for user to predict house price
import ipywidgets as widgets
from IPython.display import display

def predict_price(size):
    price = model.predict(np.array([[size]]))[0]
    print(f"Predicted price for a {size}m² house: ${price:.2f}k")

size_input = widgets.IntText(description="Size (m²):", value=100)
predict_button = widgets.Button(description="Predict Price")

def on_button_click(b):
    predict_price(size_input.value)

predict_button.on_click(on_button_click)

display(size_input, predict_button)

- The user enters a house size in square meters. - The model predicts the price based on the trained regression equation. This makes the model interactive and useful for real-world applications.

Conclusion

In this example, we successfully implemented **linear regression** to predict house prices. We learned:

• How to create and split a dataset.
• How to train a linear regression model.
• How to visualize the regression line.
• How to make predictions based on user input.

This is a simple but powerful technique that can be expanded with more features like **location, number of rooms, and house age** to improve predictions.