Advanced Residual Calculator

Calculate all types of residuals with step-by-step explanations. Supports single calculations, batch processing, and data export.

Basic Residual Calculator

Calculate basic residuals using the formula: Residual = Observed - Predicted

Calculate standardized residuals: r = e / s, where s is the residual standard error

Observed Value (y)

Predicted Value (ŷ)

Standard Error (s) Residual standard error from your regression model

Calculate studentized residuals with leverage adjustment: t = e / (s√(1-h))

Observed Value (y)

Predicted Value (ŷ)

Leverage (h) Leverage value for this observation (0 < h < 1)

Mean Squared Error (MSE) Mean squared error from your regression model

Sample Size (n) Total number of observations

Parameters (p) Number of parameters including intercept

Calculate residuals for multiple observations at once. Add rows as needed and export results.

# Observed Predicted Action

Calculate simple residuals (e = y - ŷ). Enter your observed and predicted values to get instant results.

Standardized residuals (r = e/s) normalize residuals by the standard error. Values > 2 may indicate outliers.

Studentized residuals account for leverage. Requires leverage values and model parameters for accurate calculation.

Process multiple observations simultaneously. Results include summary statistics and can be exported as CSV or JSON.

Ensure your predicted values come from a properly fitted model
For standardized residuals, use the correct residual standard error from your model
Leverage values should be between 0 and 1 (exclusive)
Large residuals (|residual| > 2-3 standard errors) may indicate outliers
Use batch calculator for efficiency when analyzing multiple observations

Learn about residual definitions, formulas, and see practical examples.

Learn Definitions View Formulas See Examples