Residual Calculator Formula

Understand the math behind the residual calculator. Each variable explained with a worked example.

Use the Residual Calculator

Formulas Used

Residual (e)

residual = actual - predicted

Absolute Residual

abs_residual = abs(actual - predicted)

Squared Residual

squared_residual = pow(actual - predicted, 2)

Variables

VariableDescriptionDefault
actualActual Value (y)25
predictedPredicted Value (y-hat)23.5

How It Works

Regression Residuals

A residual is the difference between an observed value and its predicted value from the regression model. Residuals are the foundation for assessing model fit and detecting problems.

Formula

e_i = y_i - y-hat_i

Positive residuals mean the model under-predicted; negative residuals mean over-prediction. In a well-fitting model, residuals should be randomly scattered around zero with no patterns.

Worked Example

An observation with actual y = 25 and predicted y-hat = 23.5.

actual = 25predicted = 23.5
  1. 01Residual = 25 - 23.5 = 1.5
  2. 02The model under-predicted by 1.5 units.
  3. 03Squared residual = 1.5² = 2.25

Ready to run the numbers?

Open Residual Calculator