Lasso Regression Calculator

Lasso Regression

Lasso regression (Least Absolute Shrinkage and Selection Operator) is a variant of linear regression that includes L1 regularization for feature selection. It can shrink some coefficients to exactly zero, effectively removing less important features from the model.

How It Works

Lasso regression adds a penalty term to the ordinary least squares objective function. This penalty is proportional to the sum of the absolute values of the coefficients, which encourages sparsity in the model.

Objective function: minimize(||y - Xβ||² + α||β|₁)

Where:

• y is the dependent variable vector
• X is the feature matrix
• β is the coefficient vector
• α is the regularization strength (alpha)
• ||β|₁ is the L1 norm (sum of absolute values of coefficients)

When to Use Lasso Regression

Use lasso regression when:

• You want automatic feature selection (some coefficients become exactly zero)
• You suspect many features are irrelevant or redundant
• You want a simpler, more interpretable model
• You're dealing with high-dimensional data where the number of features exceeds the number of observations

Choosing the Right Alpha Value

The alpha parameter controls the strength of regularization:

• Low alpha: closer to ordinary least squares, more features retained
• High alpha: more regularization, more features eliminated

Use the alpha slider to find the optimal balance between model complexity and performance.

How to Use This Calculator

Enter your data below as comma-separated values. For single feature regression, use x,y pairs (one pair per line). For multiple features, use x1,x2,...,y format where the last value is the target variable. Adjust the alpha value to control regularization strength and feature selection.