In [1]:
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score
import numpy as np

# Load the dataset
file_path = "housing.csv"  # Update the path if needed
housing_data = pd.read_csv(file_path)

# Feature and target selection
X = housing_data[["median_income"]]
y = housing_data["median_house_value"]

# Train the linear regression model
model = LinearRegression()
model.fit(X, y)

# Predict using the model
y_pred = model.predict(X)

# Plotting the regression line
plt.figure(figsize=(10, 6))
plt.scatter(X, y, alpha=0.3, label="Actual data")
plt.plot(X, y_pred, color='red', label="Regression line")
plt.xlabel("Median Income")
plt.ylabel("Median House Value")
plt.title("Linear Regression: Predicting House Value from Median Income")
plt.legend()
plt.grid(True)
plt.show()

# Evaluate the model
mae = mean_absolute_error(y, y_pred)
rmse = np.sqrt(mean_squared_error(y, y_pred))
r2 = r2_score(y, y_pred)

# Print evaluation metrics
print("Model Performance Metrics:")
print(f"Mean Absolute Error (MAE): ${mae:,.2f}")
print(f"Root Mean Squared Error (RMSE): ${rmse:,.2f}")
print(f"R-squared (R²): {r2:.4f}")
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Model Performance Metrics:
Mean Absolute Error (MAE): $62,625.93
Root Mean Squared Error (RMSE): $83,733.57
R-squared (R²): 0.4734

Interpretation of Results¶

  1. Mean Absolute Error (MAE):
    The model’s predictions are, on average, about $62,625 off from the actual house values. While this is a sizable error, it’s somewhat expected given the wide range of house prices in the dataset.

  2. Root Mean Squared Error (RMSE):
    The RMSE of $83,733 indicates that larger errors are penalized more heavily (since RMSE squares the errors). This shows there’s still quite a bit of variance in the house prices that the model isn’t capturing.

  3. R-squared (R²):
    An R² value of 0.4734 means that 47.34% of the variation in house prices can be explained by the median_income feature alone. This suggests a moderate relationship. There’s a clear trend, but it’s not strong enough to rely on median_income as the sole predictor.