How to Use:

• Adjust the polynomial degree slider to control model complexity
• Use L1 regularization (Lasso) to encourage sparse coefficients
• Use L2 regularization (Ridge) to shrink coefficient magnitudes
• Click anywhere on the plot to add new data points
• Use "Generate New Data" to create 5 random points
• Use "Clear All Data" to remove all points
• Observe how regularization helps prevent overfitting

Mathematical Foundation:

L1 Regularization (Lasso): Adds ${\lambda }_1\sum |{\beta }_i|$ to the loss function
• Encourages sparse solutions (some coefficients become exactly zero)
• Useful for feature selection

L2 Regularization (Ridge): Adds ${\lambda }_2\sum {\beta }_i^2$ to the loss function
• Shrinks coefficients towards zero but doesn't make them exactly zero
• Helps with multicollinearity

The regularized loss becomes: $\text{Loss}=\text{MSE}+{\lambda }_1\sum |{\beta }_i|+{\lambda }_2\sum {\beta }_i^2$

Understanding Regularization Effects:

• High polynomial degree: Creates complex curves that may overfit without regularization
• L1 regularization: Watch coefficients become exactly zero - automatic feature selection
• L2 regularization: Smooths the curve and reduces oscillations
• Bias-variance tradeoff: Higher regularization increases bias but reduces variance
• Optimal balance: Find the sweet spot between underfitting and overfitting