Hands-On Regression with Scikit-Learn

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1. Setup & Environment Imports#

To build and evaluate a reproducible regression workflow, we import numpy and pandas for numerical operations, scikit-learn for data generation, model fitting, scaling, and evaluation metrics, and joblib for model artifact persistence.

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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Scikit-Learn modules
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score

# Serialization
import joblib

# Plot styling
%matplotlib inline
plt.style.use('seaborn-v0_8')

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2. Dataset Synthesis & Statistical Inspection#

We generate a synthetic multivariate regression dataset mimicking continuous property valuation. Generating controlled synthetic data ensures full reproducibility without relying on external file downloads.

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# Generate synthetic regression dataset with controlled noise
X, y = make_regression(
 n_samples=1000,
 n_features=3,
 noise=10.0,
 random_state=42
)

# Structure into a clean Pandas DataFrame
feature_names = ['Square_Footage_Index', 'Room_Count', 'Property_Age_Years']
df = pd.DataFrame(X, columns=feature_names)
df['Target_Valuation'] = y

print("First 5 rows of dataset:")
print(df.head())

print("\nSummary Statistics:")
print(df.describe())

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3. Train-Test Splitting (Generalization Safeguard)#

To evaluate generalization capability on unseen samples, we partition the dataset into independent training (80%) and testing (20%) splits.

Never evaluate model performance on training data. High training accuracy often masks severe overfitting and provides zero guarantee of real-world generalization.

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# Partition into train (80%) and test (20%) splits
X_train, X_test, y_train, y_test = train_test_split(
 X, y,
 test_size=0.2,
 random_state=42
)

print(f"Training split shape: {X_train.shape} features, {y_train.shape[0]} target values")
print(f"Testing split shape: {X_test.shape} features, {y_test.shape[0]} target values")

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4. Feature Standardization & Leakage Prevention#

Standardizing features to zero mean ($\mu = 0$) and unit variance ($\sigma = 1$) ensures numerical stability.

Data Leakage Prevention: Always compute scaler statistics (fit_transform) exclusively on the training set, then apply those frozen statistics (transform) onto the test and production sets.

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scaler = StandardScaler()

# 1. Fit and transform exclusively on training data
X_train_scaled = scaler.fit_transform(X_train)

# 2. Apply training parameters to unseen test data
X_test_scaled = scaler.transform(X_test)

print("Standardization complete. Feature mean:", np.mean(X_train_scaled, axis=0).round(4))
print("Feature variance:", np.var(X_train_scaled, axis=0).round(4))

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5. Model Fitting & Coefficient Interpretation#

We initialize Ordinary Least Squares LinearRegression and optimize weights using the closed-form Normal Equation $(\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \mathbf{y}$.

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model = LinearRegression()

# Train the model
model.fit(X_train_scaled, y_train)

print("Model training completed successfully.")
print(f"Learned Coefficients (Weights): {model.coef_}")
print(f"Learned Intercept (Bias): {model.intercept_:.2f}")

# Interpret feature impact
for name, coef in zip(feature_names, model.coef_):
 print(f"• {name}: {coef:+.2f} per 1.0 standard deviation change")

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6. Out-of-Sample Predictions#

Generate predictions on the held-out test set using the scaled feature vectors.

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# Predict continuous targets
y_pred = model.predict(X_test_scaled)

# Comparison table (first 5 samples)
comparison_df = pd.DataFrame({
 'Actual Valuation': y_test[:5],
 'Predicted Valuation': y_pred[:5],
 'Absolute Error': np.abs(y_test[:5] - y_pred[:5])
})

print("\nActual vs. Predicted Sample Comparison:")
print(comparison_df)

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7. Model Evaluation Metrics (MAE, MSE, RMSE, R²)#

We compute quantitative regression metrics across the test distribution to validate model performance:

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mae = mean_absolute_error(y_test, y_pred)
mse = mean_squared_error(y_test, y_pred)
rmse = np.sqrt(mse)
r2 = r2_score(y_test, y_pred)

print("-" * 50)
print(f"Mean Absolute Error (MAE): {mae:.2f}")
print(f"Mean Squared Error (MSE): {mse:.2f}")
print(f"Root Mean Squared Error (RMSE): {rmse:.2f}")
print(f"Coefficient of Determination (R²): {r2:.4f}")
print("-" * 50)

if r2 > 0.8:
 print("Excellent fit: The model explains >80% of variance in test data.")
elif r2 > 0.5:
 print("Moderate fit: Baseline captured, hyperparameter or feature engineering recommended.")
else:
 print("Suboptimal fit: Underfitting detected.")

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8. Model Artifact Persistence with Joblib#

Save both the fitted model estimator and the fitted preprocessor pipeline to disk for subsequent production microservice deployment without retraining.

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# Persist estimator and scaler
joblib.dump(model, 'regression_model.pkl')
joblib.dump(scaler, 'regression_scaler.pkl')

print("Serialized artifacts saved: regression_model.pkl and regression_scaler.pkl")

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9. Production Inference Simulation#

Simulate receiving a new, raw real-world data point, preprocessing it through the loaded scaler, and generating an instant prediction.

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# Load persisted artifacts
loaded_model = joblib.load('regression_model.pkl')
loaded_scaler = joblib.load('regression_scaler.pkl')

# New unseen property listing [Square_Footage_Index, Room_Count, Property_Age_Years]
new_sample = np.array([[5.0, 3.0, 10.0]])

# Apply loaded scaler
new_sample_scaled = loaded_scaler.transform(new_sample)

# Generate prediction
predicted_val = loaded_model.predict(new_sample_scaled)[0]

print(f"Input Features: {new_sample[0]}")
print(f"Estimated Valuation: ${predicted_val:,.2f}")

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10. Residual & Parity Visualization#

A parity plot compares observed vs. predicted targets. Data points aligning closely along the identity line ($y = x$) represent high model fidelity.

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plt.figure(figsize=(9, 5))
plt.scatter(y_test, y_pred, alpha=0.6, edgecolors='none', color='#2563eb', s=40, label='Test Observations')
plt.plot([y_test.min(), y_test.max()], [y_test.min(), y_test.max()], 'r--', lw=2, label='Ideal Parity (y = x)')

plt.xlabel('Ground Truth Actual Target')
plt.ylabel('Model Predicted Target')
plt.title('Regression Parity Plot: Actual vs. Predicted')
plt.legend(loc='upper left')
plt.grid(True, linestyle=':', alpha=0.6)
plt.tight_layout()
plt.show()

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11. Pipeline Engineering Summary#

In this hands-on guide, we executed a complete end-to-end regression pipeline:

1. Data Generation: Created clean, structured synthetic data with known noise parameters.
2. Splitting: Protected test integrity via strict train-test separation.
3. Leakage Control: Scaled features using training statistics exclusively.
4. Estimation: Fit an interpretable OLS linear estimator.
5. Diagnostics: Quantified residual distributions via MAE, RMSE, and $R^2$.
6. Deployment: Persisted pipeline artifacts with joblib for zero-latency inference.