Ridge Regression 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.

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Higher values of α increase regularization strength. When α = 0, ridge regression is equivalent to ordinary least squares.

Data Input

Format: Each line should contain 1 feature values followed by 1 target value, all comma-separated.

Ridge Regression

Ridge regression is a variant of linear regression that includes L2 regularization to prevent overfitting. It's particularly useful when dealing with multicollinearity in the data.

How It Works

Ridge regression adds a penalty term to the ordinary least squares objective function. This penalty is proportional to the sum of the squared coefficients, which helps to shrink the coefficients towards zero (but not exactly to zero).

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

Where:

  • y is the dependent variable vector
  • X is the feature matrix
  • β is the coefficient vector
  • α is the regularization strength (alpha)
  • ||β||² is the L2 norm (sum of squared coefficients)

When to Use Ridge Regression

Use ridge regression when:

  • Your data has multicollinearity (highly correlated features)
  • You're concerned about overfitting with ordinary least squares
  • You want to keep all features in the model but reduce their impact

Choosing the Right Alpha Value

The alpha parameter controls the strength of regularization:

  • Low alpha: closer to ordinary least squares (may overfit)
  • High alpha: more regularization (may underfit)

Use the alpha slider to find the optimal balance that minimizes both training and test error.

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.