Purpose

Initial Rows: 300 observations with no exclusions during preprocessing
Retention Rate: 100% \u2014 all records passed quality checks and remained in the final dataset
Rows Removed: 0 \u2014 no missing values, duplicates, or outliers were filtered
Train/Test Split: Not explicitly documented, though 10-fold cross-validation was used for lambda selection

This section identifies the optimal regularization strength (lambda) for the LASSO model through 10-fold cross-validation. The lambda parameter controls the trade-off between model complexity and predictive accuracy—a critical decision that directly impacts which predictors are retained and how well the model generalizes to unseen data.

Key Findings

Lambda Min (0.085): Achieves the lowest cross-validation MSE (~24.76) but produces a more complex model with all predictors potentially active, risking overfitting.
Lambda 1SE (0.661): Selected for final model; provides comparable performance within one standard error of minimum while eliminating 2 predictors, yielding a simpler, more interpretable solution.
Cross-Validation Stability: MSE ranges from 24.76 to 153.38 across lambda values, with tight confidence bands (upper/lower bounds) indicating stable fold-to-fold performance at optimal lambda.
Final RMSE (5.03): Reflects the prediction error achieved using the selected lambda.1se regularization strength.

Interpretation

The analysis demonstrates a classic regularization trade-off: lambda.min minimizes error but at the cost of model complexity, while lambda.1se sacrifices minimal predictive power (~0.01 MSE difference) to achieve substantial simplification. This conservative choice aligns with the principle of parsimony—retaining only 4 of 6 predictors while maintaining strong cross-validated performance (R² = 0.834).

Context

The 10-fold cross-validation design ensures robust lambda selection across multiple data splits. The narrow confidence intervals at low lambda values suggest the model's performance is stable and reliable at the chosen regularization level.