● Successfully implement Ridge, Lasso, and Elastic Net regression models using the Scikit-learn library in Python.
● Apply K-Fold cross-validation as a standard and robust practice to obtain consistent and reliable evaluations of model performance.
● Experiment with different values for the regularization strength (the alpha parameter) to empirically understand its impact on model complexity and generalization performance.
● Systematically compare and contrast the behavior of model coefficients across different regularization techniques (Lasso's sparsity vs. Ridge's shrinkage).
● Analyze how regularization, as demonstrated by your practical results, helps in preventing overfitting and significantly improving a model's ability to generalize to new, unseen data.

1. Data Preparation and Initial Review:
2. Load Dataset: Begin by loading a suitable regression dataset. A good choice would be one that has a reasonable number of numerical features and a continuous target variable, and ideally, some features that might be correlated or less important. Examples include certain real estate datasets, or a dataset predicting vehicle fuel efficiency.
3. Preprocessing Review: Thoroughly review and apply any necessary preprocessing steps previously covered in Week 2. This is a crucial foundation. Ensure you:
   • Identify and handle any missing values. For numerical columns, impute with the median or mean. For categorical columns, impute with the mode or a placeholder.
   • Scale all numerical features using StandardScaler from Scikit-learn. Scaling is particularly important before applying regularization, as it ensures all features contribute equally to the penalty term regardless of their original units or scales.
   • Encode any categorical features into numerical format (e.g., using One-Hot Encoding).
4. Feature-Target Split: Clearly separate your preprocessed data into features (often denoted as X) and the target variable (often denoted as y).

1. Implementing Ridge Regression with Cross-Validation:
2. Model Initialization: Create an instance of the Ridge regressor from Scikit-learn.
3. Define Alpha Range: Create a list or NumPy array of different alpha values (these are the hyperparameters controlling the regularization strength for Ridge). Choose a wide range to explore the impact, for example: [0.01, 0.1, 1.0, 10.0, 100.0].
4. Cross-Validation Strategy: Define your cross-validation approach. Use KFold from Scikit-learn to specify the number of splits (e.g., n_splits=5 or n_splits=10). It’s good practice to set shuffle=True and a random_state for reproducibility.
5. Evaluate with Cross-Validation (for each alpha): For each alpha value in your defined range:
   • Use the cross_val_score function from Scikit-learn. Pass your Ridge model, your training data (X_train, y_train), your cross-validation strategy, and the desired scoring metric (e.g., scoring='neg_mean_squared_error' to maximize the negative MSE, or scoring='r2' to maximize R-squared).
   • cross_val_score will return an array of scores (one for each fold). Calculate the mean and standard deviation of these cross-validation scores for that specific alpha.
6. Visualize Results: Create a plot where the x-axis represents the alpha values and the y-axis represents the mean cross-validation score (e.g., average R-squared). This plot is invaluable for visually identifying the alpha that yields the best generalization performance.

1. Comprehensive Comparative Analysis and Discussion:
2. Summary Table: Create a clear and well-organized summary table (e.g., using Pandas to display a DataFrame in your Jupyter Notebook) that lists the training set performance (e.g., MSE and R-squared) and, most importantly, the held-out test set performance for:
   • The baseline Linear Regression model.
   • Your optimal Ridge model.
   • Your optimal Lasso model.
   • Your optimal Elastic Net model.
3. Coefficient Comparison Deep Dive: Discuss the qualitative differences in coefficient values across all the regularized models. Specifically, highlight the unique effect of Lasso in setting some coefficients to zero, and whether Elastic Net exhibited similar or different sparsity behavior.
4. Performance Interpretation: Based on the robust test set performance metrics, discuss which regularization technique appears to be most effective for the specific dataset you used in this lab. Provide well-reasoned arguments for why one might have outperformed the others (e.g., "Lasso performed best, suggesting that many features in this dataset were likely irrelevant," or "Ridge was more effective, indicating the presence of multicollinearity where all features were somewhat important," or "Elastic Net provided the best balance in this scenario due to a mix of irrelevant and correlated features").
5. Impact on Overfitting: Finally, reflect on the overall impact of regularization. How did these techniques (Ridge, Lasso, Elastic Net) help to reduce the gap between training performance and test performance, thereby successfully mitigating the problem of overfitting? Use your observed results to support your conclusions.